I really think that you should keep pressing this issue with your doctor (s) becuz you are young and this should be investigated. My doctor told me when I lost my menses for several months that this shouldn't be let go becuz -- it could lead to health problems like endometriosis, which could interfere with fertility down the road. He put me on a hormone for 6 months which did bring my menses back.
Now, I am 51 y/y and they are on and off again, but that is becuz I was in peri-menopause before (from age 46 y/o and on). Since you are only in your early 20's, I think this would warrant you pressing for clear answers. Yes, your weight can affect your hormones and in turn, your cycles, but that might not be true in your case; only more testing could say for sure ...
I hope you get some answers to your queries soon!