Hello! Congratulations!
I was in the overweight category when I got pregnant with my first, and probably obese with my second (got pregnant right away after the first). Everything went fine. I definitely had my fair share of aches and pains throughout the pregnancies, especially the 2nd. I don't know how much of that was because of the extra weight, but I would guess that didn't help things much. I also didn't do much in terms of physical activity, and I'm sure that didn't help much either. I would say to try to stay active at least a little...go for walks, that kind of thing.
I never had anything like gestational diabetes, high blood pressure, or anything else.
Definitely let your doctor know your concerns. S/he can probably refer you to a nutritionist and provide advice about how much weight you should gain and how to eat while pregnant.
Oh, and a BIG piece of advice I wish I had. When I was pregnant with my first, I had morning sickness pretty bad and lost a couple of pounds in the first trimester. Then in my second trimester I REALLY made up for it. Man. I think one month I gained 9 pounds and that really freaked me out. What I wished someone told me was that the weight gain would not continue on that level in the 3rd trimester. I put on almost all my weight in the 2nd trimester. (That's not exactly how it happened the second time around, the 2nd and 3rd trimesters were almost switched).
When all was said and done, I gained about the same weight both pregnancies, even though the pattern was different. I think the body kind of knows what it needs to do. So talk to your doctor and nutritionist about the best way to eat, but don't necessarily get stressed out about it either. You have enough to worry about when you're pregnant!
Anyway, I'll stop babbling now. Good luck!