Welcome to the forum!
Its a good question and hopefully an owner can chime in who has either weighed at a CAT scale or owns a Sherline. In the meantime, you can simply take the GRWR of the trailer and multiply by 13% to get an estimate of the tongue weight.
An even more accurate estimate is to take the brochure dry weight, add in an estimate for any factory options, add in the weight of propane and a battery, and then estimate your cargo, food, water, etc. This will be less than the GVWR (better be). Take 13% of that number.
I use 13% as the rule is 10-15%. I've tried lighter (steering too light) and heavier (felt wrong) and 13% works better for my TV/TT combo but YMMV.
DW, 3 Kids and our Goldens
2012 Shamrock 233S
2008 Toyota Sequoia 5.7L 4WD