Is there a relationship between Diduk and Didukung?

'dukung' is the base word.
https://kbbi.web.id/dukung

dukung/du·kung/ v,
duduk di punggung atau di pinggang orang:

'to sit on someone's back/waist'

mendukung/men·du·kung/ v
1 membawa sesuatu atau seseorang di atas punggung; menggendong:
2 ki menyokong; membantu; menunjang:

'mendukung' is the active verb.
The first definition is the literal one: 'carrying someone on your back'.
The second definition is more figurative: 'to support, to help'