Before we get into that though normally I see people increasing the weight they're lifting as much as they can. Natural progression in the gym is seen to be an increase in weight. If you don't increase your weight then you're not getting fitter or stronger surely? Not quite right. There are other aspects that you can observe to see if you're getting fitter and stronger too. One of which is range of motion. If your ROM increases then you can celebrate that as success - you're more flexible, stronger and have greater control. It's not just about lifting heavier and heavier.
In fact, I often see people sacrifice their range of motion in order to lift heavier. Take squatting for example. It's tough to be strong with a nice deep squat (getting your bum nice and low) but if you make your squat shallower (don't get as low) then you can lift a lot more weight. I think in most cases this happens without people realising it - they put more weight on and don't focus on getting a good ROM.
Well, have a look at the study below and you'll see some interesting reading. It shows that sticking with a larger ROM before increasing your weights actually has better impact on your body than increasing weight with a smaller ROM. How interesting!
Next time you're in the gym or completing a workout look to increase your range of motion (using the full range available to your joints and muscles) instead of just slapping more weight on. If you already lift heavy but have poor ROM then think about dropping the weights down a bit (de-loading) and increase your range of motion. You can then work your way back up, keeping to full ROM.
Finally though, think about technique. Adding weight generally starts to make maintaining good form more difficult and the same can be said for increasing ROM. Make sure as you do either that your technique remains solid and you don't put yourself at increase risk of injury through poor form. If you have any doubts then ask me and I can watch you to see.