Yes you need to add more weight forward of the wheels. In my tt we used under the bed and the pass thru to help. We also will put some things like an extra cooler if we have it in the front bedroom. I have seen as little as moving a 25 lb object from the back of the tt to the front of the tt. Also, 6100 lbs dry can be a lot of weight for some half tons (you didn't say so I'm guessing you have a 1500). I would weigh your combo. Weigh the truck by itself with each axle on a separate pad. Then weigh the truck with the tt attached and wdh not hooked up. Finally weigh the truck with tt and wdh hooked up. When weighing truck and trailer you want each truck axle on a separate scale pad and both tt axles on the third scale pad. For Cat scale
you can do first weigh for $9-12 and then each reweigh is usually $1-2 in a 24 hrs period. Bring a long ice scraper or broom handle to push the button as it is very high up. You will need to tell them first weigh vs reweigh and private vehicle. If they still need a number, give them your favorite number.
These weights will tell you if you are truly within TV specs, what your true tongue weight is, and if you need to readjust your wdh. The goal with the wdh is to return the tv front axle to as close to unhitched weight as possible without going heavier. Do all of your weighing loaded with a full tank of fuel and all passengers, pets and gear you would take camping. You can keep crossing the scales til you get your numbers right. IMHO small price to pay for a good handling rig.