I've found a variety of answers from doctors about losing weight. "See a nutritionist." "Lose weight. (period)" "You're overweight." "You've got the stomach flu and are carrying too many books to class" (the misdiagnosis of gallbladder attacks that led to me giving up on doctors until I nearly died)...
I've found a lot of doctors just don't know you very well. In fact, the doctor I'm most comfortable with and talk to the most is my chiropractor, and that's because I've seen her on a weekly basis for the past few months. While not a g.p., she's in great shape herself, and we have good discussions, and she's not against any of the stuff I'm doing to lose weight.
She said since my hips are out of alignment, I might want to take it easy on the cardio machines (no incline), but since my back hasn't been hurting for a while, I've been adding it in slowly, and I've been doing some deadlifts, lat-pulldowns, and abdominals to strengthen my back. (She says these are great when I told her I was doing them).
But she also gives me food and workout advice, but more as a fit 'n healthy woman living the life than in an official capacity as a doctor; but it's just nice to have that kind of rapport with a doctor of any sort, so I at least know I'm not doing something whacky or obviously bad. I wish I had that kind of relationship with my primary care physician, but it seems like it's a 6 month waiting list for anything with her...
Not being a sufferer of migraines, though, I'd just have suggested dehydration, as that's what usually causes headaches with me. (But you said water wasn't the issue).
--Janis