For example you could have a hat with pieces of paper in it each with a number. The numbers sum to 0 (some are positive, some are negative). Each person draws a piece of paper, adds his or her weight to it, then says that number. The numbers that each person says are summed and that's the total sum.
E.g., say that the random numbers are uniformly distributed between -200 and 200. If somebody says a number like 425, then I know they weigh at least 225 pounds. And the probability they weigh more than 225 - k pounds is 1 - k/400.
Then you would probably get more information from looking at the person thank you could from hearing a weight number that could be +/-2000 pounds
Then knowing any individual number (weight + pad) mod n gives zero knowledge (I think. If all but one party reveal their pads, they can trivially determine the other's weight so it fails. Believe it to be secure if only 1 party is malicious, though. Cases for other numbers of bad actors are more complicated...)
There might be behavioural issues here though - perhaps people would keep generating a random number until they are provided one that makes their weight look 'better' (and 'better' probably means 'smaller' for most people).
Edit: comicjk made a great point about large numbers. Perhaps using large random numbers (eg a normal distribution with a mean of 4550 and a std deviation of 20-30) would help reduce the behavioural issue.