If you say "people" (plural) then you can say "their" for example:

You shouldn't talk to people about their weight.

However, if you are referring to one person you have to say "his or her" because you don't know if the person is a female or male. For example:

You shouldn't talk to a person about his or her weight.

However, because this is a general statement, the first sentence sounds more correct. In other contexts, it is good to know the rule for the singular person as well. For example, as a teacher, I often have to say something like this:

It is important that a student focuses on his or her grades and studies the best he or she can.

:) Hope this helps!