regards bungee jumping

How accurately must the weight of the jumper be known?

I'd say it depends on

(a) how much clearance you need at the bottom of the jump
(b) how accurately you know the strength of the cord
(c) how accurately you know the elasticity of the cord

(a) because if you have a 100' drop and a 15' cord, there's little chance of collision
(b) because if you have a 100-lb strength of cord and a 200-lb jumper, you're likely to break the cord
(c) because if your cord is too stretchy, it will allow the jumper to crash at the bottom