Luggage when travelling with children

I think your best bet is to get some luggage that can be attached together. That way, each adult can wheel along 2-3 pieces together, whilst still being able to take them apart to check in individually.

As an aside - the reason for the 20-25kg limit (varies slightly between airlines) is that beyond that the airline normally has to pay extra to the airport for handling it. Cases much beyond about 20kg need special handling, such as multiple people to lift them safely. If you check a heavy bag, it'll almost certainly have warning labels added to it about the weight.

So, luggage you can attach together. There are two broad types here, those that were made with this in mind, and those where you can make it work!

A lot of airline crew luggage is designed to attach together, and you'll often see them wheeling a suitcase with another on top through the airport. Here, the aim is usually to keep both pieces within the cabin baggage size limit, and if it's a long trip they then attach the second one. Typically these attach by one joining on to the handle of the other, so you end up with a very tall suitcase. That said, these are normally smaller cases, so you may struggle to find large ones that'll do the same thing. You can also get ones where they attach with the largest sizes touching, to effectively give a very deep suitcase. A quick google only shows a luxury brand doing this, but I'm fairly sure I've seen others about.

Otherwise, you just need two fairly similarly sized suitcases, and some straps. Put one strap on the floor, stand the two cases together, wrap it around and tighten, then add a 2nd one the other way. Carefully tip forward onto the wheels of the bottom one, being aware that the centre of gravity is now likely off, and wheel away! (Note - don't just attach them at the top, otherwise the first time you corner or hit a bump, it'll probably go horribly wrong...)

Oh, and there is another option - many airlines allow their frequent travellers to check in heavier luggage without fees. Generally only the higher tiers, so you'll need to be doing a lot of flying to hit it... Oh, and many airlines also wave heavy bag fees for premium cabins, but that means expensive tickets!