I also find weight training really helps me deal with stress. I highly recommend it.
For wrist and elbow pain from computer use, however, weight training made it worse for me. At that time I did a bit of googling and for RSI seems like rest and stopping the repetitive motions is best. The exercises irritate the same nerves. To solve the issue, I switch to a trackball instead of a mouse. (To be clear, weight training was miraculous to me when I first started, but for RSI, fix the cause)
Changing my keyboard got rid of the immediate pain I had been experiencing for months. I started weight lifting at around the same time. The only reason I attribute lifting as being part of the solution is that I went back to typing on my laptop again after 6 months.
I now do quite a lot of typing on my laptop (90% of the software I write) and I no longer have any pain in my wrists.
This advise is probably not for everyone, I just offer it up as an interesting anecdote. If you have persistant wrist pain, its probably best to go see a specialist.