Without specifying what you're doing exactly, it's hard to say this is an actual problem.
There's a common misconception that utilizing a lot of memory is bad. However, unused memory is a waste. It's like keeping a warehouse mostly empty because you think it's cleaner. By keeping as much as you can in memory, it saves having to go to disk and also reloading content needlessly. As long as the program is good about letting go of memory it doesn't absolutely require to other programs, it's not a problem.
If it's a memory leak on the other hand, that would be a big problem. You can check this by closing all your tabs except say a blank one. Then start loading other memory intensive programs. If you have another browser installed, like Chrome, start loading massive pages in it. If Firefox is still showing massive memory usage, then it's a leak. Your system will likely become sluggish from the other programs demanding unavailable memory.
It might be Firefox, but often it's an add-on or combination of add-ons causing the leak. You can disable all add-ons by starting Firefox in safe-mode from the terminal, firefox -safe-mode, to see if you have the same thing happen.
If you're saying that with just a few "light" websites open, and not doing anything in Firefox, that Firefox just starts taking up more and more memory, then it's plausible it's just Flash or some script going nuts. This is why I put "light" in quotes. It's unbelievable how badly some simple-looking sites are designed.
Best Answer
Fiefox has a small memory leakage problem
To fix it [Try This]
Open Firefox and go to the Address Bar. Type in
about:configand then press Enter.Right Click in the page and select New -> Boolean.
In the box that pops up enter
config.trim_on_minimize. Press Enter.Now select True and then press Enter.
Restart Firefox.
Hope this will help