I have a Takena 2265 and have towed with full tanks. Not sure of the 1865, but with mine the tank is just in front of the axle so it doesn't add much tongue weight (maybe 1/4 of the weight on the tongue, 3/4 on the axle).
But as mentioned, I don't tow with a full fresh (or gray) tank any more than I have to. Depends how far and what the likelyhood of getting fresh water at the destination is. If it's a campground where I can fill up on the way in (water thief hose adapter!) or even carry about half a tank and use the spigots and haul a couple 5-gallon jerry cans to top up I will do that.