using phrase "weekend of"
I'd argue that in the given month, the 'weekend of the 24th' is a misnomer; Monday is not normally a weekend day at all. Friday evening (the 21st of the given month) might just be counted as part of the weekend. And if it is a holiday weekend, then Monday might scrape as part of the long weekend, but normally, you would only reference a date that is part of the weekend.
Personally, I would not talk about the weekend of the 24th:
S_M_T_W_Th_F_S
16 17 18 19 20 21 22
23 24 25 26 27 28 29
30 31
I would say the weekend of the 22nd or 23rd.
Also the weekend of the 29th or 30th.
The week of the 24th has weekend days of the 23rd and 29th, those are the days that are on the ends of the week that contains the date of the 24th.