I tow our 3,100-lb dry camper with my lifted GX (Ironman FCP and 32" tires) regularly. With gear and water, the camper is probably closer to 4,000-lb, and then we have a family of 4 inside the GX (so total weight above empthy/stock is probably 4,500-5,000 lb considering I have some armor). The GX is a great tow platform for smaller campers - we've towed ours up to 700 miles in a day without a problem, and mine can tow our camper 70-75 mph on the interstate without too many issues. I do have several towing-related upgrades including LT headers, a Nomad valve body, bigger trans cooler, and a torque converter lockup switch. I use a weight distributing hitch, which is essential when towing with a short-wheelbase platform like this.
However, I think the issue you will run into is the already somewhat tall gearing issues of the GX made worse by 35's. When towing my GX has a hard time pulling 5th gear on anything but totally flat ground below 70 mph, and 4th gear results in something like 8-10 mpg vs. 11-13 mpg in 5th gear. With 35's you'll probably be in the 3rd-4th gear most of the time and have problems accelerating from a stop and have very limited passing power. I can accelerate OK with 32's, but I think a stock-geared GX would be very, very slow on 35's with a camper hooked up to the back.
So if you are serious about towing anything other than a popup camper and keeping the 35's, I'd probably budget a re-gear for your GX (which is also a good time to add lockers). Transmission upgrades are also a really good idea and will help you tow as well without cooking the transmission. The stock cooler is undersized and the torque converter does not lock up in 3rd gear and below, which can make it easy to overheat the transmission on a long climb (I also recommend monitoring trans temps with an app like Torque Pro).
FWIW, when my 32's wear out I am going to upgrade to 33's and 4.56 gears to help with towing and off-road performance.