I started using the clear corrugated poly that is sold for greenhouse use. I saw it used somewhere on the net just as I was thinking about lids for my last few tanks, and the stuff is great. It's cheap, does not discolour or fog, can be easily cut with a pair of shears, can be drilled for feeding holes or other openings. It does not bend or bow the way plexi does when exposed to humidity on one side.
Aside from the safety aspects of broken shards after a big fish strikes a glass top (been there...), it is also safer for the fish themselves. If they strike a heavy sheet of glass there is no flex or give to it, and the energy of the collision goes right into their heads...unless of course they break the glass. The clear poly is very light weight, so when a big fish hits it the lid easily flexes and moves, dissipating the energy of the blow; they will never break it. It's like the difference between running into a concrete wall (glass lid) versus running into a wall of 3/8-inch plywood (poly lid). Neither one feels good, but the thin wooden wall is much easier on you than the solid concrete one.
Your 8x3x2 tank has the same dimensions as a number of plywood tanks I have built over the years. The sections of the lid are large enough that a big fish is unlikely to completely knock one off and leave the tank, even without weights. Or, if you are concerned, you could make the lid one piece of poly. This would be a bit more awkward, but would still be light enough that a single person can easily handle it, but even harder for a fish to dislodge and knock off.