Here is what I could find for that camper and your 2013 Honda Pilot.
Let's start with the camper. In our FILES section, we have copies of many of the Sunline sales brochures, which lists a lot of good info on the campers. Look up at the top of the found screen for the words FILES, Click it when logged in, and you end up in the files section with lots of good Sunline stuff.
The 1997 T-2053 brochure listed the base "dry" weight as 3,465#. And a dry tongue weight of 390# (3,465# - 3,075# axle weight = 390# tongue weight). The dry weight does not include a battery (Approx 50#) or the LP gas in the LP tanks. If you still have 20# LP tanks, the gas adds approx 42#. If someone upgraded to 30# tanks, it would add 63#.
390# + 50# + 42# = 482# tongue weight with no cargo in the camper, BUT there is always a but...
Added options are not included in the dry weights. In 1997, they had the preferred options group (POG); if yours has an air conditioner, that item was part of the POG, and the added weight is not reflected in the dry base weight as it was an option. Then there is a spare tire, crank-down stabilizers, and options that add weight.
I am not 100% sure if the 1997 Sunline had inside the camper a weight sticker that called out the actual weight the day it left Sunline. You can look for it; it is inside a top kitchen cabinet, bathroom cabinet, or even a bedroom cabinet.
The dry weight might turn into 3,700 to 3,800# GVW and the tongue weight between 480# to 520#, pending what it is you have for added options even with no added camping gear.
There is also a rating on the truck for the frontal area of the trailer. This is the size of the trailer exposed to the wind, as wind drag is real when towing a travel trailer. Towing a 3,700# boat will usually pull easier than a 3,700# 8 ft wide 9 1/2 ft tall travel trailer when you get up to highway speeds. We nickname towing a camper, towing a brick... Some manufacturers list the frontal area at 60 sq ft, others 50 sq ft. It all depends on the manufacturer. When you exceed it, the performance of towing will diminish. The truck works harder to try and keep up. I can't find that rating for your truck.
If you want, I can go deeper into this; just ask, and I'm glad to, but I see this for your truck. I listed the above to see where this is coming from to help you learn safely.
The good news is you have a light load in the truck with only two passengers and no cargo; that helps.
There is an issue with the tongue weight; you can be 30# to 70# over the truck hitch rating. And they do not allow a weight distribution hitch to help overcome the heavy load on the back of the truck. Being tongue heavy means the truck's front end is light, and stability is not as good. The hitch itself is beyond its rating.
I'm unsure how long you have to tow to get to the Catskills or where and high up. I used to live in that area, and some parts are "up there" compared to the lower Hudson Valley. The Catskills is a big beautiful place.
I will sum it up as this; your truck will be at its pull limits with the frontal area issue combined with the camper weight. Your fuel mileage will be cut in half, which is typical, but the drive train will work hard to sustain 55 mph to 60 mph. The camper tongue weight is an issue, not being able to use a weight distribution hitch. You will find the back of the truck sagging; how much is yet to be determined? Honda did have a limit to now exceed in truck sag. See page 331 in the manual.
Here is something to think about as an option; see if it fits you.
You are going to only tow the camper once to its resting place. You have to buy or find these items to tow it.
A brake controller is to be installed in the truck. This is a must, do not attempt to tow the camper without it. Here is one of the better brands/types. You may also need a connection cable for plug-and-play if they offer one for your truck. https://www.etrailer.com/Trailer-Bra...sha/90195.html
Not sure if you will install the controller or hire it out. Members have done both in the past. There is a setup and a small learning curve on how to use the brake controller. It is not rocket science, but it will take some time.
You must acquire a 2 5/16" tow ball rated at least 5,500# to fit the camper ball coupler and the correct sized draw bar to level out the camper hitched to the truck. Do not try to tow the camper using a 2" to ball, it can come off.
You need to acquire towing mirrors; the 8 ft wide camper will block your rear view without tow mirrors that extend beyond the camper.
You can add up those costs and how to sort them out. As an option, do you have a buddy who has a full-size pickup truck, even a 1/2 ton truck, that is equipped with a brake controller in it, and they have towed trailers before? Giving them money may be cheaper than getting your truck up to the task. Or hire someone to tow it for you.
If this is your first time towing a travel trailer, there is a learning curve, and your truck is at its max. Again, not sure how far you are going, 15 miles or 150 miles, the 150 miles can be a really long trip, and then there is how high up in the Catskills you are going.
I will also add this in case you did not know. Check the tire date codes; trailer tires are different than auto tires that can have lots of miles on them. Trailer tires often age out before they ever wear out. You can't tell that the trailer tires are OK just because there are lots of tread left and think it is a good tire. Tire age helps tell if the tire is OK to tow. See if you can find the DOT date codes and how old they are. A tire blowout dealing with 6-plus-year-old tires can make camping a bad day. If you need help reading or telling the tire age, let us know, and we can help show you how to do that. And for sure, regardless of age, ensure the tires are aired up to the cold side wall max pressure listed on the side of the tire before heading out. If you see many cracks in the sidewalls or between the tire treads, that is another sign the tire is getting old or too old, pending the size and qty of the cracks.
Feel free to ask about the above items, towing, or anything on the camper. I'm giving you this straight up to help explain what you may be up against and try not to have you learn the hard way.
Hope this helps,