What would a Shakespearean audience think of a man so heavily influenced by his wife

Weak.

Explanation:

They would think that he shows weakness and such, in those times women were known to do more domesticated jobs such as cooking and cleaning. When a woman is shown to be more dominant in a relationship in shakespeare they are thought to be weak and almost scared.

Coward

Explanation:

They would believe that he was not able to fulfill any thing because he needs his wife to be there for him every time.