Fattening metallic ends of jump wires
For industrial applications, ferrules are commonly used.  They are metal sleeves that get crimped onto the ends of wires where connections will be made:


(sorry for the big picture!)

Their main purpose is to gather up all the strands of a stranded wire, and give a good, solid connection for use with screw terminals or clamp-style connection points.  But, for your purpose, they should add some thickness to the wire.

I don't believe that multiple layers of solder will work, because each subsequent application will reflow all of the solder present, and won't stack up...