A weight distributing hitch/bars will move a couple hundred lbs of hitch weight from the ball to the truck's front suspension. A couple hundred and that's all! Helps but doesn't allow you to go much heavier at all. Don't forget the weight of the hitch as that is also added cargo as is anything carried in the bed of the truck. 1270 lbs capacity even for a 1/2 ton truck is a very low capacity and paltry. Remember that you need roughly 12% of the loaded TT's actual scaled weight on the ball to be safe and pull with very limited TT fish tailing. At 10% you are really pushing the limits and just that 2% makes all the difference in towing a TT. Wind buffeting from a passing truck for instance can make you grease your britches real fast if you don't have enough weight on the ball! White knuckle towing isn't any fun at all!
No way with a 1/2 ton with 1270 lbs capacity would I haul an advertised base dry weight TT with over 5500-6000 lbs max and then having it actually scale weighed on a truck scale (very cheap) for it's true dry weight. Why? as said, passengers, hitch, any other cargo carried in the truck itself, any and all options added to the TT's base advertised dry weight which does not even include batteries or propane either which are also weight on the ball hitch, water in tank and water heater or anything in the holding tanks, anything you load in the TT - all food/canned goods/clothes, tools and camping supplies-items/hookup and leveling needs/you name it, all add weight and it adds up so fast!
Even with this dry weight, you will be at or over your truck's 1270 capacity loaded and ready to travel. Do your own math and it will enlighten you real quick!
Very seldom will a brochure stated base dry weight be even close to an RV's actually scaled dry weight when you purchase it and drive it away and that's still well over a thousand lbs + less than when actually loaded to travel for the RV alone.