I have set up a limit location constraint, and when I move it upward, it doesnt move instantly, it looks stiff, then it decides to move. If you require me to provide an attachment of sorts please do ask.

Thanks in advanced

Its the distance set. The object location or transform or something is already past the limit.
If you move the object and it is stoped by the limit and you move it more, you will then need to move it back to the limit before you see it move past the limit.