I agree that there is no way you'd want to hang a 1/2" thick 4'x4' acrylic on the wall with just VHB tape. Way too heavy. You can usually get the weight of the piece by talking with your supplier, in case you want to use the weight to plan what types of hangers will hold the appropriate weight. But VHB alone for that size acrylic will not work. I like Signman315's recommendation of securing a backboard of some sort directly to the wall with suitable screws/anchors, and then mounting a much thinner piece of acrylic to that. And I would double up VHB with silicone.
We recently did a two-layer piece of a acrylic for a customer where the top layer was 1/8" acrylic with a 2nd surface print on the back, backed with white vinyl. We then had a 3/16" piece of acrylic behind that, and we were able to silicone the two pieces together -- the silicone did not show through the back of the 2nd surface. This sign was only 10" tall by 30" wide (actually 14 of them), and we were using the standoffs to mount them, so no mounting concerns for ours. But letting you know that the silicone BEHIND the white vinyl which was behind the 2nd surface print, attaching the two acrylic panels together, was not visible from the front of the signs that we just did.