Does an mp3 player with more music weigh more?

No. The MP3's on your MP3 player are stored as a series of 1's and 0's in the player's memory. basically, a 1 corresponds to a switch that is turned on, and a 0 corresponds to a switch that is turned off. Your MP3 player has millions of these switches, and adding music simply changes the pattern of which ones are turned on and which ones are turned off. The switches are already there-- adding music only changes their state.

In short- no, adding music won't make your player weigh more.