Set shipping price by weight?

I have products that are available in any quantity the customer chooses. They will be delivered by EMS, therefore the shipping price does not increase linearly with the quantity. In other words, an order of 5kg costs less to ship per kg than an order of 1kg. Is there any way to set this up?

Sure. You can go in the menu System->Shipping methods and in the manual shipping plugin, you can create several shipping methods with all your different prices:

from 0 to 4.5kg => $10
from 4.5kg to 8kg => $20
etc...