If I buy 1 Product ... then later I buy 2 of the same Product ... is the shipping doubled?

If so, you might look into the Per Unit perweightunit shipping module that allows you to set the Shipping Cost as the products_weight on a per Product basis ...

So if you set the Product Weight to 1.25 then:
1 x 1.25 = $1.25
2 x 1.25 = $2.50
3 x 1.25 = $3.75

and this will follow for all Products in the order ...