Weight of welds is (almost) neglible) since a weld in a thick piece of ajoining plates (and pipes) needs a bevel prep on both surfaces, and the final result by any competent welder will end up as an almost smmoth surface. So, the net weight change is almost zero.
The only additional weight from welding would happen if a root gap exists between pieces, fittings, or plates: and that root gap should be very small anyway. (HP pipe joints should have a consumable backing plate or griout-out backing ring anyway: still, no net gain in weight.
What could help in a BOM is the total linear length of weld: how many feet (meters) of weld is required: That number can be used to directly get a cost additional factor, since the time for each pass of a weld is depend on length of the joints, not size of bead.
For tanks, the length would be the total length of all joints between plates (including head plates to wall plates for a flat roof or sloped roof tank).