First of all I have never used freezer paper for paper piecing as it is too heavy and stiff and I can think of no advantage to using it. The thinner your paper is the better. Tissue paper is good but hard to use in a printer for copies. Cheap news print works fairly well and squares of "sandwich wrap" are great if your printer cooperates and you cut it to the right size. It is available at Smart and Final stores or restaurant supply stores, otherwise I use the cheapest light weight copy paper I can find.
The only use I find for freezer paper for quilting is to iron white muslin to it for photo copies in your printer or using double thickness fused together for applique. :)