From a girl's standpoint (a 30 something girl that is!) you do have a difficult subject ahead of you.
How about encouraging her to talk about her feelings about her family and their weight issues? How weight has affected them and everyone around them and specifically their outlook on life, etc.? Allow her to vent about that and then slowly try to work towards how she is feeling now without exactly saying - hey, your gaining some weight and it is scaring me.
I suppose telling her over and again that you love her for her and not anything else would really help. Maybe if you can help her to connect to why she is eating more, ask her why she gave up the vegan, how she feels about eating disorders, etc. My suspicion is that there is so much more going on. If she can make the emotional connection to why she is gaining weight then maybe she will get back to a healthier lifestyle again without you ever having to say the words, hey your gaining some weight...hope this helps some...