Welcome aboard! Lots of info above. A quick Google search says you should not use a WDH with a Pilot. Now that was a generic search, not knowing which year you have. Something may have changed over the years. I recommend reviewing your TV owners manual, there will be a section on towing. If it is not recommended, I would use at minimum a friction sway bar.
Attached is the spec sheet for your 260BH. The key number to look at is the GVWR. That is the max weight the TT is designed to carry. The empty/dry weight is generally useless as it is only that way when it is delivered to the dealer lot. They are delivered without propane in the tanks or a battery.
https://www.jayco.com/rvs/travel-trailers/2024-jay-flight-slx/260bh/
I recommend opening the TVs driver's door and look at the stickers. One of them will give you the payload capacity for your Pilot as it rolled off the production line. The payload capacity is the key thing to look at. This takes in the tongue weight of the trailer, the stuff and people in & on the TV.
Being a bunkhouse model, I suspect you have kids, and kids grow, and they bring a LOT of stuff with them.
For the TV, I recommend adding up the weight of everything you will bring with in/on the TV, such as the kids, DW, pets, luggage inside the TV, including your DW's purse, kids toys, booster seats, firewood, cooler, activity bag, hitch components, etc. If you do not know your actual tongue weight, use 15% GVWR (900 lbs). Per Jayco the dry hitch weight is 515 lbs, so you know you will be north of that. Compare this sum to the payload sticker. I suspect you will be overloaded.
The tongue weight should be between 10 and 15 percent of the actual weight of the TT. If your tongue weight is to light the trailer can sway easily and cause a major accident. To heavy and it can affect your steering, and again cause an accident. None of this accounts for how it affects the engine and transmission life.
1,370- 1570 lbs guess of what your payload might be:
0 lbs - DW - most vehicles give a 150 # allowance for the driver
200 lbs - DH
150 lbs - 2 kids - young and still growing
50 lbs - dog
50 lbs cooler
20 lbs kids activity bag in TV
75 lbs kids toys/bikes, etc that is in the back of the Pilot
50 lbs stuff you normally keep in the TV, or mods you have added.
75 lbs - WDH
700 lbs tongue weight, maybe up to 900 lbs after a year or so
1,370 -1,570 lbs.
You might be within capacity or might not be. My old Dakota, I was very close for many years, and was hard to keep the TT and TV on a diet.
Good luck and happy camping
