I don't know that saddle width is the simplest or most likely culprit; this is, after all, a used bike, so the saddle could be worn unevenly from the previous owner, or there might be a problem with bent rails, or a cracked shell...
I'd first inspect the bike closely and verify the seat seems symmetrical (e.g. not leaning to one side, padding equally dense side to side) and is in proper order (not cracked underneath; rails not bent or seat post clamp touching bottom of saddle). I'd also affirm the saddle is oriented straight ahead, and not angled to one side or the other.
It's also not your weight, though it may be the way you're sitting on the bike for some reason, so just consider what you're doing as you're riding, for example, favoring one leg over the other. It could be a mild scoliosis, or a leg length imbalance, or some other physical condition.
If those things check out, and your reasonably comfortable that something with your body isn't going on, I'd go ahead and start playing with saddle selection. If you can't get comfy on the one you have now, it may be that you're sitting on it oddly trying to make it feel better.