Weight Based Shipping isn’t integrated with WPML. It’s unnecessary since WPML can automatically capture the titles of delivery options from any shipping method with the String Translation module.
Make sure to trigger the delivery options to appear on the cart or checkout pages first. Otherwise, the String Translation module won’t “see” them.
You may need to reset caches, rebuild indexes, re-scan translations, etc., to “refresh” WPML.
The following threads in the WPML support forum might be helpful:
– https://wpml.org/forums/topic/translation-of-delivery-method/
– https://wpml.org/forums/topic/shipping-options-not-translating/
