First of all, I wanna make sure we're all on the same page. When talking about lean I'm referring to the body fat percentage of an individual that should be in the recommended range.
The range/recommendations will depend on many factors, mainly gender, age, height, and weight. Other factors are also taken into consideration, such as if an individual is a professional and/or lifetime athlete. These groups will be able to maintain a fairly "low" bodyfat throughout the year without much effort.
Related - Calculate Your Body Fat Percentage
Why You Should Stay Lean
#1 - Bodyfat anatomy and physiology
Fatty tissue is a special form of connective tissue which has the capability of storage. Individual fat cells have a round shape which is responsible for the grainy appearance of fat.
Fat cells mainly store triglycerides (chemical compounds that can be visualized as a trident, where the base of the trident is glycerol and the spikes attached to the base are fatty acids) and vitamins. They can also temporarily store byproducts and water (still debated though).
From an anatomical standpoint we can divide fatty tissue as followed:
Yellow fatty tissue, divided furthermore into:
Storage fat, which the main purpose is storing reserve energy. It can store up to 3/4 of the energy compared to regulars fats that we ingest due to it being comprised of minerals, vitamins, carbs, proteins, and water along with fatty tissue.
Structural fat which fills out empty space and protects organs (perirenal space), reduces pressure (fat on the sole of our feet), and is used as a placeholder (female breasts). This type of fat is covered in collagen fibers.
Brown fatty tissue is found in infants and hibernating animals and has a very high energy value
From a physiological standpoint, we can further identify subcutaneous fat (body fat) which is stored in skeletal muscles and visceral fat around organs. This is responsible for most if not all health risks associated with high body fat percentages.
#2 - Constant cell number
Fat cells are unique because the amount number never decreases. The number of fat cells increases during childhood and adolescent years, finally "stabilizing" in adulthood. 
"The fact that fat cell amount can be increased but not decreased most likely contributes to the body’s drive to regain weight after weight loss.” This is a quote from Dr. Kirsty L. Spalding, a cell biologist at the Karolinska Institute in Sweden and author of "Dynamics of Fat Cell Turnover in Humans.” 
The cells expand to a certain volume when there is an excess of energy in the body in an effort to store it. Only after reaching a max volume of one cell a new cell will be formed.
Like most other cells in our body, fat cells (adipocytes) have a lifespan. Even so, their turnover rate is around is "perfect" meaning they die off and get replenished at the same speed. Around 10% of our total fat cells are switched out on a yearly basis.
#3 - How fat cells are formed, they influence the rest of our body
As mentioned above, new fat cells only form when the maximum storage volume of the previous cell is reached. Until the max volume is reached cells are filled up with triglycerides which are neutral fats.
Triglycerides are the most common type of lipids (fats) in nature and have become synonymous with the macronutrient some fear and some praise. If someone is mentioning fats, they are probably referring to triglycerides.
There are two ways we can promote fat storage:
- By consuming too much fat.
- By consuming (way) too many carbs.
The first way is far easier to achieve and far more efficient in the body. It's as simple as eating too much fat which will lead to the body directly saving it into fat cells.
The second way is far more complex and less efficient since carbs don't have the right form (they aren't triglycerides). The six-step transformation process is very inefficient and has certain pre-requirements (full glycogen storages, extremely low fat and very high carb diet).
The amount of carbs we have to ingest during a day to force the body into lypogenesis (the metabolic formation of fat) is roughly around +500g. 
The main reasons this number is so high are:
- The body's adaptation to the high carb intake raising the glucose oxidation capacity (the number of carbs our body can process).
- The activity of the enzymes (PDH - Pyruvate dehydrogenase, ACC - Acetyl-CoA carboxylase) that are required in the transformation is very low.
- The process is very energy inefficient (up to 1/4 of the energy provided by carbs is used for this process).
Other than serving as an energy reserve and changing one's appearance, fat cells also have an important physiological function. They secrete leptin. Leptin is an anorexigenic signal. It gives our brain signals to eat less.
#4 - Why staying lean is a good idea
It is known that a high body fat percentage, which in most cases means high visceral fat, increases the risk of pretty much every disease out there. By staying lean you decrease your risk of the following:
Insulin resistance (IR)
"In particular, it has been argued that abdominal obesity, specifically an increase in visceral fat volume, is the fundamental culprit responsible for insulin resistance and associated abnormalities. Mechanistically, it has been proposed that enlarged visceral fat cells secrete a number of inflammatory cytokines that lead to insulin resistance." 
Insulin resistance is the first step towards diabetes.
As mentioned above leptin regulates our hunger and tells our brain when we are full so we don’t eat.
"Indeed, obesity promotes multiple cellular processes that attenuate leptin signaling (referred to here as “cellular leptin resistance”), and which amplify the extent of weight gain induced by genetic and environmental factors." 
"There is current debate regarding whether body weight variability is associated with cardiovascular events. Recently, high body fat percentage (BF%) has been shown to be a cardiovascular risk factor." 
"In obese individuals, the amount of nonesterified fatty acids, glycerol, hormones, cytokines, proinflammatory markers, and other substances that are involved in the development of insulin resistance, is increased.” 
"Obesity and type 2 diabetes are becoming increasingly prevalent worldwide, and both are associated with an increased incidence and mortality from many cancers." 
Other than the obvious health benefits of being lean there are also others:
Better quality of life
Leaner individuals have far fewer inconveniences during everyday activities like dressing up, working, tying shoes, walking etc.
Decreasing body fat is much easier
As we already know the number of fat cells does not decrease unless you decide to do liposuction. Even then the weight loss reverses itself mostly within a year either through increase fat cell number or fat cell volume. 
This is the reason individuals that have been at a normal or lower body fat percentage throughout their lives can manage and/or decrease their body fat levels much easier. Once those cells are formed, no matter how much you deplete them through dieting and exercise they still take up space and show up as "limp fat."
Developing and refining your fitness/nutritional skills
With all the stress of the 21st-century people forget that we have been eating for hundreds of thousands of years, and that we will continue to do so in the future. Nutrition is the most influential factor when it comes to our health and it can even alter our genetical code.
Staying lean and active while having a hectic schedule is very challenging. It forces us to find better and more efficient ways to sort out and optimize our nutrition so we can enjoy all the health benefits of a normal body fat percentage.
Lower life cost
People like to argue how a healthy diet is expensive and hard to sustain financially. When we look at it from a prevention standpoint it's the cheapest option we can choose.
A healthy lifestyle is the best prevention method. It will save us a lot of money in the long run because hopefully, we won't need healthcare - or more precisely sick-care. We might even save some money on insurance rates.
References1) Spalding KL , et al. "Dynamics of Fat Cell Turnover in Humans. - PubMed - NCBI." National Center for Biotechnology Information, www.ncbi.nlm.nih.gov/pubmed/18454136.
2) "Ernährung und Stoffwechsel“ – Dörr, Martin
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4) "Obesity and Leptin Resistance: Distinguishing Cause from Effect." PubMed Central (PMC), www.ncbi.nlm.nih.gov/pmc/articles/PMC2967652/.
5) "Associations Between Body Fat Variability and Later Onset of Cardiovascular Disease Risk Factors." PubMed Central (PMC), www.ncbi.nlm.nih.gov/pmc/articles/PMC5378370/.
6) "Mechanism Linking Diabetes Mellitus and Obesity." PubMed Central (PMC), www.ncbi.nlm.nih.gov/pmc/articles/PMC4259868/.
7) Gallagher EJ and LeRoith D. "Obesity and Diabetes: The Increased Risk of Cancer and Cancer-Related Mortality. - PubMed - NCBI." National Center for Biotechnology Information, www.ncbi.nlm.nih.gov/pubmed/26084689.
8) Pischon T and Nimptsch K. "Obesity and Risk of Cancer: An Introductory Overview. - PubMed - NCBI." National Center for Biotechnology Information, www.ncbi.nlm.nih.gov/pubmed/27909899.
9) Seretis K , et al. "Short- and Long-Term Effects of Abdominal Lipectomy on Weight and Fat Mass in Females: a Systematic Review. - PubMed - NCBI." National Center for Biotechnology Information, www.ncbi.nlm.nih.gov/pubmed/26210190.