I think its tough to make too strong a prediction not knowing the new CBA and what that will do with the market this summer, but in general, I am very worried about giving him a long contract.
I think he is pretty close to his ceiling already, and I am afraid he will want more money than his production and role entails. More importantly though, guys carrying that much weight scare me as they get older. Particularly guys who are effective largely because they are just a tiny bit quicker than other big men.
As he gets into his later 20s, it is going to be harder for him to keep that weight off, and carrying that extra weight is also going to take its toll, both on his body itself, and on that quickness.
I think a good comparison is Antoine Walker, who was a very effective player inside in his early years, despite the fact that he played below the rim, and used quickness to sneak the ball up to the basket. But, as he got into his upper 20's, that quickness advantage diminished, and those shots became blocked more, and he was no longer beating guys to the rebounds, which ultimately drove him more and more to the perimeter.
Regardless of how hard Davis works at keeping the weight off, I am afraid this is pretty innevitable, and given his lack of length, it might not be long before he is struggling to be a productive NBA player.
I think, if they can get him for maybe 2-3 years, at a reasonable price (in todays market, I would say about $4 million per year, but that will change depending on the CBA), then I certainly sign him. Anything more than that, and I think I would have to let him walk.