Upvote:3
“European flights” are a vast topic, with dozens of airlines each having their own policies.
The most restrictive are usually the low-cost carriers (LCCs), with the largest ones (Easyjet and Ryanair) by default (without paying extra) only allowing one single item of the “under-seat” size. They of course have different maximum sizes for these, but Ryanair apparently has no weight limit for this one while Easyjet has a 15 kg limit, though you must be “able to lift and carry it yourself”.
Unless you know the specific airlines you will travel with (and what options you are willing to pay for), it’s very difficult to give a blanket rule. Some will only allow a small item, some a larger one ( it only one), some both, the sizes will be different, and the weight limits, if they exist, will be different.
Note that while sizers for hand luggage are common, scales are much less common, especially at the gate. Years ago I know Aer Lingus could be strict with their 7kg limit if you had to go through check-in desks (where they have scales) but if you got to the gate directly nobody would mind, for instance.