My mother sees no reason to exercise help me?

My mother seems to think that i dont need to exercise. Especially today since when i went to try on some clothes in charlotte russe the size smalls were hanging off me. I told her that now clothing designers are making the size of clothes bigger bc americans are now bigger. Like smalls are really mediums and mediums are really larges(some clothing places at least) so i needed an extra small which is really a small. She thinks that because I exercise everyday i am becoming too focused on my weight. I exercise to be HEALTHY not bc i wanna lose weight. I am 98 pounds and 5'1 i have always been skinny my dad was skinny as well so losing weight is not on my mind avoiding diabetes that runs in the family(my mothers side) is. My mother thinks i dont eat when i do i eat three balanced meals a day i make sure they are HEALTHY. I eat junk food when its around but my mom and stepdad have diabetes so having oreos around all the time is not wise. I exercise 20 min everyday which is less than they recommend.I dont throw up after i eat and i dont worry about calories as much as i do the HEALTH part of food. Ill eat a dairy queen blizzard but i wont eat one EVERYDAY. I also try to watch my sugar intake bc like i said diabetes runs in the family.Will someone please inform my mother of the benefits of exercise and that exercising 20 min a day isnt hurting me(be nice im gonna show her these answers guys) also how long and how many days of the week should i exercise to MAINTAIN my weight and to be HEALTHY? Please help shes worried and i want her to know that im only trying to be healthy.