Q. How Chashev is the idea that Shabbos Shevah Brochos belongs to the kallah? Is there an obligation on the family of the Kallah to pay for it even if they are not the hosts?
A. According to the Shulchan Oruch (E.H. 64, 4) it is the Choson's obligation to provide the wedding seudoh. However, today there are different customs; mostly the various expenses are split between the parties. (see Oruch Hashulchon ibid. 12, and Oitzer Hapoiskim ibid. f.n. 19).
There is no obligation to do Sheva Brochos the rest of the seven days if there is no minyan, ponim chadoshos or it cannot be afforded. (See: Yam Shel Shloimo, Kesuvos 1,12). Chasam Soifer (E.H. 1,122) mentions that in Krakow, in his time, they only had one Sheva Brochos. Today's tradition is to do all seven. Nitey Gavriel (Nessuin 2,83,15) mentions in the name of the Itur, that in days past it was the Kallo's family expense. This was presumably, due to the fact that the new couple would abode with them. Today, he writes, they mostly allocate and divide them between families and friends. The main issue is to share fairly in Sholom and mutual understanding. No reference is made as to why Shabbos should be different.
There is however, an indication in Talmud Yerushalmi (Beitzo 5,2) of Rebbi arranging a seudoh for his son Rabbi Shimon in Shabbos.
Horav Shlomo Miller's Shlit"a opinion is that Shabbos is not unlike the other Sheva Brochos days in this respect, and it should be allocated by mutual and peaceful agreement.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a