How do you weigh?

The question asks for a word to complete the sentence "How ___ do you weigh?". This is a question about quantity. Since 'weigh' refers to a measurement of mass, which is typically uncountable, 'much' is the appropriate word to use with uncountable nouns. 'Many' is used with countable nouns. Therefore, the correct completion is 'How much do you weigh?'.