Personally man, any time I gained weight killed my PFT score in the military. To be a decent runner (which is, you know, like 80% of the real PFT) I have to be thin as a frigging rail. I'm 275 right now, but back in the Army I was a (in my mind) terribly skinny 200.... and I kinda had to be.
Maybe youre different. I've seen some thick guys do great PFT scores... but I think theyre the exception. Keep in mind that the military wants you lean and mean, not powerlifter-y. They care more about you being able to run across a battlefield with a pack on then being able to bench 400 lbs.
Keep in mind that muscle mass, but its very nature, creates CO2. Running gets harder with the more muscle you get, not less. I dont care if its in your legs or wherever... how many stacked Kenyan marathoners do you see?
In addition, I'm guessing youre in the Marines from your PFT description. That pull-up gets ***way*** harder with more mass. I've bench well over 300, and people always say that I should be able to kill pull-ups. Yeah, right. The overall strength of my back/lats just doesnt compensate for the overall body mass.
Like other people have said, take it slow. A few pounds at a time. To repeat, the military doesn't really want you to be heavy, especially the Marines. How many big guys do you see on base? Probably not many, and for a reason.