Yes, the major carriers usually set a limit of 20kg for economy class. They can charge you excess baggage fees if your bag is overweight but most don't worry about just 1 or 2kg.
Business class passengers and those who have Frequent Flyer status have extra baggage allowance - usually 30kg.
I mentioned the 32kg. in case you were thinking that checking in as a group would mean that the kids in your group had 10kg bags and you could then have 35kg or something like that. No, it wouldn't be allowed.

If you're worried about the bags (esp. on the way out of Bangkok) you could always put some stuff in the kids' bags.

It's a good idea to join up to Thai's frequent flyer program - Royal Orchid - and when you've travelled a certain number of miles with them, you get Silver or Gold card and that gives you extra baggage allowance. This is why I have a baggage allowance of 30kg with Thai and their partner airlines.
You can get the enrolment card at the airport. Fill it in and send it off after your trip is over. Keep your boarding passes as you need to send those with the form.

7kg is the usual limit for carry-on bags but they aren't usually weighed. I guess they'd ask to weigh it if they noticed you were struggling to lift it though!!!!
I usually put valuables, fragile and small-but-heavy stuff in there (camera, jewellery, ipod, computer etc. or anything I'm not prepared to lose).
If you haven't already bought a carry-on bag, it's a good idea to get one with handles that can fit over your suitcase handle - that way you just wheel your case/carry-bag combo together and not have both hands dealing with luggage - esp. good when you're travelling with kids.