Try the Demographic and Health Survey (DHS). They have what you are looking for, for a large set of countries. On top of that you will in part be able to identify family ties, and you can even get access to geo-coded data. The data has answers to an extensive questionnaire.
You have to "apply" to get the data. But that is just a formality -- even as a undergraduate student with just a one-sentence research proposal you are likely to get access within a few hours.
Edit: The surveys consist of several modules, some modules are only administeed to female respondents, some only to children and so on. Sometimes different waves in different coutnries contain a different combination of modules. Depending on what exactly you're studying you'll need to figure out what exactly your needs are. To show you that the data exists I pick on example: Egyptian women in the 2014-wave. You'll find the data here:
Egypt: Standard DHS, 2014 >
Household Member Recode > Variables:
Here, you see a hight/weight scatter (
scatter ha2 ha3 in stata):