Honestly, how heavy do we think Josh is now? I'd bet my house that he's no longer 237 (as listed) or 240 as you suggest. If you just look at his face, he's filled out quite a bit. I'm not saying he's fat, he's just fully an adult now and no longer a kid coming out of college. Coupled with a legit NFL strength and conditioning training program and maybe a bit of the delish blue-collar food Buffalo offers; I bet he's close to 250 - 255.
A natural, world class athlete like Josh, with a large frame like he has. Could easily gain 20 - 25 lbs and if you saw him on a beach or something, it would be very hot to notice the weight gain.
Whatever he's doing, it works. As long as he doesn't lose quickness, the weight likely affords him some protection.
To answer your question, I said a cross between Elway and Favre, but this season, much less Favre. Cunningham / Elway is spot on I think- maybe with some of Kelly's on the field presence and leadership