The 2015 XLite 33RES was the biggest Cougar XLite built in 2015. At 36' in length and 11'4" tall, it's larger than many of the fifth wheels in the lineup. As such, one would expect a heavy tongue weight, especially with an optional A/C installed in the forward bedroom vent.
No two owners are going to load and tow the same, so any responses will be a "ballpark estimate" at best, and your Cougar may come close to their weights or it may be significantly different. Here are some "ballpark estimates" to get you started:
EMPTY WEIGHT: 7675 (plus optional equipment)
CARGO CAP: 2085
The tongue weight should be "somewhere" between 10% and 15% of the total weight, so empty/"at GVW" your tongue should weight: 767.5 - 1464 pounds.
With the added A/C, I'd suppose you're heavier than the "minimum" and as you stated in your post, the "yellow sticker" indicates a "shipping weight" of 8253, which is 578 pounds "heavier" than the "website specifications" (probably added optional equipment). The "shipping weight" doesn't include propane (60 lbs) or battery (40 lbs) so you can expect an additional 100 +/- pounds added to the "shipping tongue weight" even for an empty trailer.
The only "valid way" (that I know of) to get your "real world" weights is to hitch your RV as you will be towing it, loaded for a trip, and visit a certified scale. Weigh your rig to get the "towed weight", then uncouple the "distribution bars" (leave them inserted in the hitch) and weigh again. This second weight will give you the "non-distributed" weight. Then pull off the scales, unhitch, pull back on the scales to get the "truck weight". With those figures, you can get your "real world" weight. Honestly, that's the only way I know of to get an accurate weight for your rig.
Using the "scale/beam" method to weigh your trailer tongue will give you a "good ballpark" weight, but even an inch of "mismeasured beam" will significantly alter your calculations.
I'd urge you to find a scale and know what you're really towing. After all, even with an F250 diesel, you're at the "upper end" of your truck's towing capacity with a 10K/36' trailer.
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS