Another quick sketch for a gantry design would be a large double beam with the router running between them.. If you went with a 3" square 1/8" thick 6063 AL tube, it would be less than 16 pounds for a 4' gantry (1.6 lbs a foot). For a little bit more you could go with 4" square tubing at 2.2 lbs a foot. Go crazy, 6" square tube is only 3.5 lbs a foot. How on earth can you justify gantries that weigh over a hundred pounds? This is still using fairly conservative and easy to work materials. Go up to thin wall carbon steel with an engineered section and you can get a lot lighter than this. It still leaves plenty of room for a robust z axis and nothing is cantilevered out adding all kinds of funky forces into the mix.
This is not getting into really sophisticated construction techniques. It is still stuff you can bolt together. It is just looking at the properties of the materials and not just throwing huge chunks of solid materials at the problem in hopes that it will make it rigid. Spread out the footprint of the bearings to add stability. Don't cantilever things out that create big torsional forces. Use large cross section thin tubing. The idea is to reduce weight and add strength.
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