Chem Caulk 900. Belive it's made by 3M.  It's $7 for a small caulk gun size tube but sticks well to about anything. Use it to glue steel to concrete in concrete irrigation boxes. (sticks even being underwater all season, year after year. I've also used it to glue PVC pipe into Concrete.

Just curious,, is the weatherstriping for a overhead door or something?  

Just thinking the weatherstriping would last longer on the door or movable object vs: gluing to the floor.