Remove the weatherstriping first, and clean the area where it was glued down, If someone used silicone adhesive, like bath tub caulk, to try to fix it, be sure to clean off all the silicone or your paint will fish eye. If you are putting on new weatherstriping, wash the weatherstriping first with hot water. Some of the rubber weatherstriping comes with a soapy residue from being manufactured, and you will have a devil of a time trying to get it to stick to the steel unless this residue is removed. Its also a good idea to also wipe the part that gets glued down with thinner first as well. If you have a glue-down weatherstriping, use something like a plumber's solder flux brush for the adhesive - the stuff is too stiff to apply with any other kind of brush.
Any solvent that will clean up adhesive globs will also remove paint, so you want to be real careful when you brush adhesive on the rubber and on the steel. Since it's an Army truck, probably the best solution is not to worry about any globs since a small blob of glue looks a lot better than destroyed paint.