The SW and LW are usually have the heaviest swingweight of the wedges.
The SW (usually) has an larger flange on the sole to blast the ball out of the sand. LW has the shortest shaft, and the feel of extra weight helps steady it on impact. Some examples...
Callaway Forged: PW, GW = D3; SW, LW = D4
X.Hot irons in steel shaft: PW, AW = D2; SW, LW = D4
Titleist Vokey SM4: PW, GW = D3; SW, GW = D5
Cleveland 588 Forged and 588 RTX; PW = D3; GW = D4; SW, LW = D6
Again, you have to swing these wedges and see how they "feel." I'm surprised to find that Vokeys have swingweights comparable to other models. I always thought Vokeys felt too light.
As for more swingweight, if you switch to a lighter weight grip (while keeping the same thickness), this will increase the measured swingweight. A good clubsmith can calculate how much a lighter grip will increase your swingweight.