Do women have an obligation to listen to krias hatorah every week?
No, the obligation of listening to Kerias Ha-Torah does not apply to women.
According to many the general obligation of reading from the Torah is incumbent on the community (not on individuals), and therefore applies to the congregation (of men) and not to women.
Even if it is a personal obligation (the Chazon Ish was concerned for this view) it applies to men who are obligated in Torah study, and not to women.
See Halichos Shlomo, Tefillah12:6.