Sounds like you need a bigger reel.
Your reel should have a size to it, standard one's being either, #3/4, #5/6 or #7/8. Therefore if you buy a #7/8 reel it will take either 7-weight or 8-weight line plus 50 to 100 yards of backing.
Backing is there for two purposes. Firstly to give extra line to a hard fighting fish and secondly to pad out the reel to help minimise memory in the line.
Out of interest, what reel do you have and what size fly line are you putting on it?