the stuff to weld plexiglass is either
methylenchloride
or
chloroform
both the two are almost identical in their chemical structure.
(and both are anestaetics, although not in use anymore because of their side effects)
They evaporate VERY fast and have to be kept best in glass containers. Use a very thin syringe with only-plastic piston and a tiny needle (grind the tip flat)
(Rubber will grow very much in dimension under these solvents, hence use only-plastic syringes)
The amount you need is almost Nil. 50 ml will last for many weldings.
Just use a trace to put in between two closely matching surfaces and press a little. The solvent breaks up the the molecular structure (makes it fluid) so a little pressure until the solvent evaporates is sufficient. BUT the solvent can not bridge gaps. So only exactly matching surfaces (like fractures or exact planes) can be welded. If the weld shows no air bubbles or airy zones that creep in from the edges, it will have the same stability as the material itself.
WiLi