Check out this video link; it proves that Mozilla Firefox continuously increases the size of memory consumed every moment..
What's the matter?
check your add ons and plugins disable them and see if it makes a difference. I installed a gmail plugin which took over 1 gb ram when active. CRazy :-(
Alternately, clear the download history (you may need to exit Firefox and delete the file downloads.rdf file from the profile folder in some cases ) and change your Download History settings to remove files from the Download Manager "Upon successful download" to circumvent the problem
more advance options would be to change the about:config preferences below while these may have an effect on memory consumption but may also affect performance or reduce functionality
Preference Max memory freed browser.cache.memory.capacity and browser.cache.memory.enable 14MB browser.sessionhistory.max_total_viewers
All the best