The top layer on my mat is starting to curl back a bit. Anyone know the best glue to use to reattach the layers?

It all depends on what type of fabric it is. Your best bet is to head to a fabric/sewing shop and ask them. They're probably the best people to ask.

The biggest problem would be the glue soaking in and spreading and turning the area hard or discoloring.

If it isn't seperated too far in, depending on how it is made, you may be able to just trim the worn edges off and have a brand-new edge.