Question about Time Machine

Maybe I'm just ignorant, but will having Time Machine in Leopard use up a lot of memory if it has to remember files from days and weeks or however far back it goes?

Can you delete something permanently or what?

Time Machine won't eat up your memory, but it will take up HD space.
While nobody can answer you at this point with any degree of certainty, I am going to bet that there is a limit on how far back you can save.