Then I found out the "culprit" which was bugging my Firefox browser. It was Firebug. This useful tool was the one that was slowing down my Firefox indeed.
Firebug is a debugger. A debugger is program looking around for errors (bugs) in other programs. That's is the reason it makes my Firefox dragging its feet.
What I do now is when I am not using the Firebug, I just deactivate it.
That fixes my Firefox browser from slowing down.