"How will the weather be on Tuesday?"
Translation:Sut bydd y tywydd dydd Mawrth?
It should really be ...ddydd Mawrth in this sentence - the mutation then tells us that dydd Mawrth is being used in an adverbial sense, meaning 'on Tuesday'.
ar ddydd Mawrth usually means 'on Tuesdays' in general, unless a specific Tuesday is meant, such as ar ddydd Mawrth 24ain o Fai:
- Es i yno ddydd Mawrth - I went there on Tuesday
- Ro'n i'n mynd yno ar ddydd Mawrth - I used to go there on Tuesdays
- Es i yno ar ddydd Mawrth 24ain o Fai - I went there on Tuesday the 24th of May.
Not everyone makes these distinctions all the time, though, especially in informal speech, as the details are usually clear from the context of the conversation.