Welcome to JOF
I'm sure some JOF members with similar TV/FW combinations will chime in....., but I would start with a visit to your local CAT scale and confirm how much "available" payload capacity you actually have..., better then guessing.
Have your TV loaded with full fuel, passengers, and simulated cargo for an accurate CAT weight....., subtract the CAT weight from your TV's specified GVWR...., this is what you have available for a FW's "loaded" pin weight and hitch.
Manufacture's recommend a loaded pin weight in the 15% to 25% range (of FW gross weight), but 20% seems to be the norm. If you tend to pack heavy and/or full time you may want to figure 25%.
The 2016 375BHFS has a 15,975lb GVWR and a published 13,570lb UVW........, "as shipped" UVW in most cases is higher. If the FW in question is on the dealer lot, check the yellow weight sticker to confirm the actual shipped UVW.