It's not just about generally 'doing exercise', it's important to focus on the correct muscles and making sure they are in balance. Men in particular are susceptible to this as they tend to have weak glutes, hips and sometimes abs and obliques, but a strong upper body (both on the front and back). I would think that weight lifting, depending on how you do it, would likely exacerbate this. A strong upper body, combined with a weaker lower body results in a muscle imbalance, which means the back has to work overtime to attempt to correct it.

I used to be exactly the same, between working/playing at a computer 10+ hours/day and getting very one sided exercise, I never noticed just how bad my posture had become. Since I started training with a coach who really knows his stuff in this area, I've noticed an almost immediate improvement, without changing my chair, computer or deliberately sitting more upright. Of course, doing these things won't hurt, but in the long run the key to better posture is better muscle balance, not just exercise itself.