I'll chime in with what I understand and, granted, I'm just learning a few things about TTs and towing myself but have had several motorhomes and have one currently. Others can correct me where needed.
If you're looking at a new model, here is the spec' page for the 27RL:
ZT27RL - CrossRoads RV
You'll notice that the GVWR is 7,850 lbs. Then you'll see it has a dry weight of 6,520 lbs.
Since Cargo Carrying Capacity (CCC) --which I assume you meant when you referred to 1,000 lbs.-- is calculated by subtracting the GVWR from the dry weight including the weight of the full fresh water tank, the full propane tank, and the weight of passengers calculated by seating positions, the trailer you've referenced seems to indicate that the CCC will be 1,330 lbs.
Subtract 6,520 from 7,850 you'll get 1,330 lbs.
Then you'll notice that it says the carrying capacity is 1,596 lbs. but that evidently if factoring in the weight of the items mentioned, i.e.the weight of the full fresh water tank or the weight of the full propane tank.
Remember, the GVWR is the rating that the manufacturer gives to the unit which tells you what the total weight should not exceed when loaded with everything. The GVWR is assigned and will not change.
Your carrying capacity is the variable and it seems in this case, should not exceed 1,330 lbs. to be within the GVWR of 7,850 lbs.
So, we know that no matter what, if you load your trailer correctly and stay under the CCC and therefore, below the GVWR of the trailer (7,850 lbs.) and your Tundra is rated to tow 10,000 lbs, then you are substantially under its towing capacity.
However, your Tundra should list a GCWR or the Gross COMBINED Weight Rating which is the total that the two vehicles together should not exceed. On my truck, I've already looked up all three, the GVWR, the GCWR, and the maximum trailer weight as a starting point.
The next thing you'll have to determine is at what weight you can load your Tundra and still be within its GCWR. I'm thinking it will be within limits but you might check just in case.
Lots of stuff that has to be checked to make sure you're within safe weights, eh? I'm just going through all this myself with the trailer I'm thinking of towing so we can learn together.
And, we haven't even touched hitch ratings and tongue weights, etc. *ack*
I'm sure the nice folks on this forum will help us out and we'll both become comfortable with the weight "rules" of towing so that we will be safe when out there on the road.