The answer to the riddle "If a butcher is 5 feet 10 inches tall, what does he weigh?" is "meat." Butchers prepare and pack meat by weight.
Height and weight are closely related, so referencing the butcher's height in the question encourages people to think about the butcher's weight, rather than what the butcher might be weighing. The answer becomes clearer if you remove references to height from the question. For example, "What does an assistant at a butcher's shop weigh?"
A variation of this riddle could be "John is 6 feet tall, wears size 10 shoes and is an assistant at a butcher shop. What does he weigh?"