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I was in Hong Kong recently and there was nothing that appeared to be 'weekend only'. I didn't see any change in how crowded things were at weekends compared with weekdays. Hong Kong is always incredibly crowded.
We did try to visit the Hong Kong Museum of History on a Tuesday and found that it was closed every Tuesday. (It is well worth it, by the way - we came back a different day) You might find that other museums have a 'closing day' too.
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One thing that is fun is going to the 10,000 Buddhas temple:
It requires a bit of a walk and is therefore off-limits for tourist buses. There are many Buddha statues with funny faces along the way, the view is great from there, they have a vegetarian restaurant that serves quite good food which visually and taste-wise imitates classic Chinese dishes (sweet & sour chicken for example).
Another thing is going to Sai Kung and eating at one of the many Seafood restaurants. It's a bit of a way out, but the village is quite cute, there is another temple and the seafood restaurants are a real spectacle with their huge aquariums and live fish to pick from.
A walk down Hollywood road, seeing the Antique stores and the Mo Man Temple is also something more relaxed.