Actually, Shakespeare never used this specific phrase. If he had, the gramtically correct way to say it would be "I bite my thumb at thee!"
I will bite my thumb at them, which is disgrace to them if they bear it.
--Shakespeare (from Romeo and Juliet)
It pretty much mean fuck you in lamens terms, or a different way to flip someone off back in the day
I bite my thumb at thee for being such a disgrace!
This, actually means that you want to start a fight. A looong time ago people used to "bite" their thumb at someone to show that person you don't actually care about them.
I bite my thumb at thou!. I completely disagree with you all the way.
When armies took prisoners in southern Europe in the middle ages, they would sometimes be offered the chance to earn their freedom by eating a fig from a mules anus. As the captors taunted their captive, offering him this degrading method of escape, they would bite their thumbs.
I bite my thumb at thou! infidel!
It's an old English term for "Fuck you!" Is used in many of Shakespeare's plays.
I bite my thumb at thou! Thou hast beseeched thy family!
As has been noted before, it has been used by Shakespeare.
A qualified guess is that the phrase, (and the hand gesture that accompanies it), symbolizes oral sex,
and implies that the insulted is gay.
Shakespeare - "Romeo and Juliet"
a vaginal cream using in the "love-making" process
look mate! It's (hey sues)!