Not forgetting that it's not only the weight of the guitar that could be a problem here, it's where the bass sits on the strap, and the angle of your wrist while you're playing. Do you "warm up" your fingers & hand before playing? Stretching your fingers and flexing your wrist before you even start playing will help (it does for me).
If, for example, you're a particular fan of Peter Hook, you may well wear your bass quite low. This can cause big problems with the angle that your wrist has to be at in order to play the bass, and could well cause the numbness in your hand. If you wear your bass quite high, this might not be so much of an issue. Also, do you work on a computer for any length of time? I found that I tended to lean on my left elbow a lot at work, this was causing pain in my left shoulder. Once I'd realised his and sorted out how I sit while working on the computer, I don't tend to get any problems with my left shoulder any more.
Certainly, a wide, padded strap strap should help, but it also pays to think about where your bass sits on the strap, and how your hand & wrist move while playing.