So I found these adorable bandanna's at Walmart - couldn't find any material at Walmart; Hancock or JoAnn's to match or even come close....

They are the perfect size for the square I am making and they are 4 for $1.00

the PROBLEM is that the material is thin....is there something I can do to stabalize or sturdy the fabric up?

I recently used lightweight fusible interfacing on fabric from WalMart that didn't wash well. It worked well though it hasn't been washed yet. I assume it will wash just fine as the fusibles do when I use them in apparel.