Good call on getting the thicker one! The 1/8" would deflect 8 times as much at the same weight. You'd be looking at about 6.5 lbs to deflect .25" with the 1/8" thickness. The polycarbonate alone is 3.1 lbs per side for 1/4" thick (and half that for half the thickness of course).

The calculation is based on 24"x24" since what's happening on one side of the table is nearly independent of the other side.

Gluing/adhering in some way will help for sure! Good luck