Bert, you can print double-sided if you already haven't, and use the heavier paper.
You can make the type smaller and fit more than one song on a page.
Someone already mentioned getting a bigger binder.
Split up the songs into two volumes.
You can reinforce thin paper with Scotch tape along the edges with the holes - put the tape on before you punch them. I used to do this all the time with stuff falling out of medical records.