I looked into variable products, thanks for the tip. But that seems indeed a long way to get there, and it means also that I cannot let the customer freely enter the desired quantity of product, but I'd have to present the client with an (endless) list of different weights to choose from. And I am not even sure if Woocommerce would calculate than the right price, or just use the weight entered for calculating shipping... No to mention the hassle when a price (per kilo) changes...
Thank you also Filipe for your reply. Still waiting for someone to come up with a solution.