What kind of glue should I use to stick 4x4 tiles on to a wooden fold

epoxy glue would work especially if you are worried about them coming loose.

A good wood glue should work.

Wood glue will not hold ceramic tile onto a wooden table.

I do agree with the epoxy; be sure to have good ventilation for that.

Another glue that should work is Liquid Nails. I suggest the construction version. It should hold nicely.

Either of these glues will be light, too.

For all things wood.... I reach for Gorilla Glue. I've used it on just about every surface, other than metal.

E6000 will work. :)

I love liquid nails! It can be quite sticky though so use disposable gloves.

Liquid nail, Lowe's. Home depot, or Wal mart