I wouldn't describe Cynis as the weakest house; we have Tepet for that.
Cynis has strong familial ties with Houses Mnemon and Sesus, as well as more complex political Sesus ties. It's also the Guild's trade partner on the Blessed Isle. The family's power is largely economic and political rather than military; it controls the Blessed Isle's slave and drug trades, and has tons of high-society influence through its magnificent galas, legendary physicians, and reserves of blackmail material. It also has its fingers in much of the Blessed Isle's limited sphere of organized crime, and its poisoners are without peer.