Your only mistake is assuming you don't need to work out. Unless you look like Arnold Swartznegger, you could probably go for some improvement just like she. "Let those who havn't sinned cast the first stone". Besides, working with her helps in 3 ways:
1) The work out cannot hurt you, only help you.
2) It may become an activity the 2 of you enjoy doing together. (always helps in strengthening a relationship)
3) You will be there to push her and provide the support she needs.
Besides, the more overweight you get, the less likely you are to go to a gym or somewhere else public because you will be concerned about the way you look. Buff people like to go to gyms/etc and show off... overweight people do not.
Oh yea, and I don't get any sexual fantasies . The last dream I remember (2 nights ago), I was running through the woods weilding a flaming sword that was burning my hands and I was cutting dudes in half. It was totally fscked, but uh, whatever.