If we have a balanced market it should drop the same percentage that the dividend is of the share price. If it drops more, it means there is a profit in selling your shares before dividend payments, and buying it back afterwards. And if it drops less, it means there is a profit to be made in buying shares before a dividend payment and selling it afterwards.
So in a balanced market the price will drop each week by the dividends until it hits zero?

No. The price will then subsequently rise by the expected amount of the next dividend over the course of the week (at a pace that reaches equilibrium with the markets discount rate for the security).