It's about more than weight as 350+ fat boys without pop can be moved relatively easily by 310 pound non-fat boys on the offensive line.
If there were a capable DT to plug the middle at low cost to the Pats, then it is a no brainer. Take the deal. I just don't see that guy out there right now. You have broken veterans and free agents who are not good enough to play. Given various roles in defensive reserves, I just cannot think of a team (1) who has such a player available and (2) would part with the player on the cheap. You realistically would not part with a young player that represents the future for nothing, and dropping to 0 insurance on your line after an injury could put you where the Pats are now after a single play.
Not a huge fan of Bleacher Report, but this
article is probably accurate on the type of line depth expected on the 53-man roster. I also liked this
article on the BB hybrid defense, which suggests the requirements of the defense and how you cannot simply add a fat man because the schemes tend to require players shifting between roles (and with fast paced offenses limiting substitutions, even more so).
In the end, I wish there were an easy answer, but this is like Christmas shopping the evening of December 24th. What's on the store rack is picked over and not worth buying. If early shoppers bought more than they need, then they would likely sell items at a huge markup, for far more than the item is worth.