Could use a similar technique remotely using a random number generator. Provided there are enough passengers the sum would approximately equal the true total weight.

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.