We're not keeping the distinction between Driver Licence requirements and legal, mechanical safety on the road.
For driver licence - all the gross (max allowed) weights add up - to determine your required licence.
So empty or full doesn't matter.
This is silly if you're towing an empty flat-bed - but hey.
For on-the-road limits, load does matter.
You need to select vehicles - and then load them - to respect your trailer limit, each trailer axle limit, each trailer tyre limit, your hitch limit, your tow vehicle limit, your tow vehicle's axle limits and your tow vehicle's tyre limits.
Many, many recreational users get some part of this wrong - and unlike North America, cops are unlikely to carry road scales in their vehicles to assess your compliance - so it'll only be a crash that reveals your error.
For my adventures in Canada/US, I was going to buy a RAM 1500 - but I couldn't make the truck loading (and rear axle loading) work. The trailer just put too much weight (1T) on the back of the truck - via the tow hitch. So I went with the much more robust RAM 2500 - and even then used a weight distribution hitch, to transfer 350 Kg of tongue weight to the truck's front axle. Either truck was well within spec for simple tow capability (5 & 7.8 T), but I needed the 2500 for the axle loading and for the all-up weight of what my truck would carry over & above the trailer.
Weight distribution hitches (ie: Reece) are cool engineering - but (as far as I have seen) almost unheard of in NZ.