Could increase the weight bonus of the gym pass. It is annoying to open storage 20 times instead of possibly one.
Genetics do not really have an advantage. with 50x exp rates you can make your own with 130 str in half an hour and unlock all areas with skip books, I have a mechanic specifically for this purpose.
The only effect I can think of in keeping weight limit low is to make you spend time opening storage multiple times, which costs a few zeny each time.