>>891274>the metal has warped because of the heat from welding....100% truth
this problem was why spot-welding was invented; it allows joining thin sheet metal pieces without warping them, because it only heats them up over a small spot for a few moments (it is ugly, but that wasn't the main goal...)
Even if you don't weld a flat sheet of metal to anything else, it can still warp just from being unevenly heated to such temperatures.
OP: if you wanted it perfectly flat, you done ruined the first try. You're not going to be able to get it to sit straight now, ever. If you have an angle grinder, you could cut the thicker sheet's edge off (maybe a quarter-inch) so it is slightly smaller... but it may still have warped from the heat. It may be good for other things but you won't get it flat again.
Brazing would be better to use to prevent warping, but you still can't run long seams like that, or even, run seams all the way around the thick piece. Warping is guaranteed.
My suggestion: get some screws, cut the heads off, and then BRAZE them to the back-side of the (new!) thin sheet, and then drill holes in the (new) thick sheet to match the studs, and use nuts to hold the thick and thin sheets together.... this way you aren't running any long beads at all.