2 year olds do NOT need fat free food. (healthy) Fat is ESSENTIAL for brain develop. Not to mention that it is partially the fat that cues the stomach/brain for satiety (fullness).
Children that age will NOT overeat healthy foods. If your child is constantly asking for food, he's _hungry_. Stay away from extremely low-fat foods and start introducing things that are higher in the good fats. Obviously no trans-fats or saturated fats, etc. You might try introducing some kind of nuts or seeds that are loaded with the good stuff - peanuts, almonds, sunflower seeds, etc - depending on your comfort level and food allergy concerns.
If your child is not eating junk food and is only eating healthy foods, you have nothing to worry about. Listen to your doctor. How big are you and your husband frame-wise? If you are tall/average, your child may just be following your genetics.
My three are TINY. My husband's family are all short and skinny. My almost 6 year old isn't even 40 pounds yet. And she eats anything and everything. My just about to turn 4 year old is 36" tall and 29 pounds soaking wet. My youngest (the only boy) is much heftier than the girls ever were at his age, but compared to other kids he's dinky. In contrast, my cousin's son is 3 and he's taller and heavier than my almost 6 daughter.
http://www.cdc.gov/nchs/about/major/nhanes/growthcharts/c... This link is to the CDCs website and they have charts to track growth for children from birth on up to 5 years or so. http://www.cdc.gov/nchs/data/nhanes/growthcharts/set2clin...
At 27 months and 36" high, your son is hovering aroun the 50th percentile according to the chart. That's average. He's about the 97th percentile for weight, but that could mean anything. He could be about to hit a growth spurt and shoot upwards. I've found that they don't grow up AND out symetrically. It's one then the other. So the get heavier and then they get taller. I REALLY wouldn't worry.