I would use 'on' because a weekend is two days (or more). 'At' is more particular, for a smaller place or shorter time, whereas on/in are used for longer durations or larger spaces. "Let's eat at an Italian restaurant at 9pm" against "Let's eat in downtown on Friday".
Going by this logic, 'on' should be used.
'The' is imperative because weekend is a common noun, and to add specificity to it, we use the article the. 'The' denotes person(s) or thing(s) already mentioned, under discussion, implied, or otherwise presumed familiar to the listener or reader.
So you should use 'the' too.
Hence, from your choices, F is the correct answer.
D could make sense too, if you have been disturbing someone for many weekends. So your 'disturbee', for lack of a better word, would know that you acknowledge the fact that you disturb him on most, if not all, weekends.