When my son was born, he didn't sleep well, so I didn't either. My wife has a career and I was an equal partner in his care. It didn't help that I was working 80+ hours a week on something that was key to the success of the small company I worked for. Add in stress eating, and cutting out exercise due to perceived lack of time, and I gained 10-15lbs a year until my son was 4 or 5.
My son is 13 now, and its only in the last few years that I've really started to take care of myself. I've started exercising, stopped eating junk, and tried to make time for sleep. The result is I've lost 60lbs over the last few years, and am in better shape than I've been since highschool. However, I still don't sleep as well as I did before he was born.
My advice to new dads is: Take care of yourselves. Eat right. Don't cut out exercise to save time.