My thoughts, for whatever they're worth...

I don't have experience with either the 640 or the 640 Pro. I will say that for several years my "grail gun" has been the 640 no-dash. I think having a steel J-frame has a lot of merit if you already have a lightweight snub. I belt carry 99.9999999999% of the time, so in that sense the weight difference between a 340 and a 640 wouldn't make much difference (not that I wouldn't notice the difference, just that it wouldn't make much difference to me). I do like the idea of carrying a lightweight snub and having a similar, but heavier, steel snub for the bulk of my practice (periodic practice/training with the lightweight snub would still be necessary). It would also make longer training courses more comfortable.

The difference is really in the sights (the Pro is cut for moon clips, but that's a moot point for me). I prefer my self defense guns to have, essentially, the same sight picture, which is one of the reasons I prefer plain black sights. I was curious so I compared the M&P 340, 640 Pro, and 640. As it turns out, both the M&P 340 and the regular 640 have pinned front sights, so it looks like you could get the same front sight mounted on the 640. The front sight on the 640 Pro is dovetailed, plus it has the 2-dot tritium rear sight.

So, if I were in your position, I would get the regular 640 as a supplement to the M&P 340. Then I would have the same front sight as the M&P 340 installed on the 640 (I have neither the tools nor the skills to do it myself). Paint the 640's rear sight black to match the 340's finish, and you have two guns with the same sight picture, a light one for regular carry and occasional practice and a heavier one for regular practice and carry at other times. Or, if you felt the need, carry both.

Just my opinion.