Ace,
The other guys have done a good job explaining this (much better than I could), but basically the drag does increase as the line on the spool decreases.

If you own any Shimano Tiagra's and still have the boxes and owners manuals, there is a GREAT diagram of this in there. Inside the owner's manual they go through the exact physics of the whole thing with pictures and explanations on why you should back the drag off when a fish takes a lot of line off the reel.

Bryan