I have 45k miles on my 35" Toyo M/T's, and I am having this very same internal debate since I need to replace them in the next month or so.
Although I do think 37's and the right amount of lift (4" ballpark) look very nice on the vehicle from an aesthetic standpoint, I think that's really the only thing in favor of going that route.
I have seen a whole host of issues on rigs running 37's that I have never had to deal with running 35's. Death wobble, bump steer, ball joint failures, rubbing at full flex, etc. That said, I believe driving style has as much to do with these issues as the tire size, so I would take it with a grain of salt. I do not believe there is a hard "maximum" you can run with a D44, it completely depends on how and where you drive. A D44 will push 37's all day long on the freeway without issue :ylsmoke:
I'm also pretty convinced that in real-world wheeling, and especially expedition type driving, the difference in capability between 35's and 37's is minimal. I have always been able to follow rigs running 37's anywhere I wanted to go.
I think I am coming down on the side of replacing my 35's with the exact same tire, since I have been extremely happy with them overall. My 2 cents.