One factor is what your ticket / status gives you. The other factor is that on midhaul aircraft in particular the overheads simply are not big enough for everyone's bags, and there are safety concerns at the higher weight of overheads when full too. Now these are very different factors, but to a passenger with checked bags it amounts to the same thing. So had you turned up at the gate with very large bags, maybe a bit over the limits that TAP advertise, they will want them in the hold on full flights. They are not bothered about charging for that, unless you are really being silly about it.

But i'ts reasonably clear where we are here: Discount gets one bag checked if Star Gold, other bags have to go hand luggage. You risk having to pay if they are over dimensions, so you can't complain if you get a hefty bill, but sometimes they are ok to let it slide if you help them by swiftly getting bags into the holds. If you don't want to risk the hefty bill then buy the ticket with the right allowances, if it was 4 big bags for 2 people, Discount doesn't seem to me the right fare bracket for you.