Methinks the Premier doth protest too much

Hamlet Act 3, scene 2, 222–230

The principal meaning of "protest" in Shakespeare's day was "vow" or "declare solemnly", a meaning preserved in our use of "protestation".

When we smugly declare that "the lady doth protest too much," we almost always mean that the lady objects so much as to lose credibility.

Gertrude says that Player Queen affirms so much as to lose credibility. Her vows are too elaborate, too artful, too insistent.

More cynically, the queen may also imply that such vows are silly in the first place, and thus may indirectly defend her own remarriage.