How do so many online tea shops have free shipping?

In those cases shipping costs are just built into the price of the teas.

Not having free shipping also causes many online retailers to shrivel and die : )

When you offer free shipping on all products, sellers calculate approximately how much will the shipping cost and add it to the product price. Unfortunately, just like buying donuts, the more you buy the cheaper they get, so when you buy more then 2-3 products your total price as customer is high and the sellers shipping may not be that much. In the end most customers shop around and if the total price is high, they will simply go somewhere else and not buy anything at all. It’s better to show clear product price right from start and shipping at the end. Free shipping usually works as a promotion when the seller will forgo some profit in hopes that customer will purchase more products and in the end seller makes some money that way.

They up the price of the tea a bit to compensate for having to pay all our part of the shipping cost. The reason they do this I figure is probably too avoid a situation where the shipping costs almost as much as the tea, as this tends to make people second guess their purchase.