What gearing does it currently have? Typically 3.73 or 4.10.
Assuming you have 3.73 gears stock then running through a gear calculator states 4.30 gears are needed to compensate for 37" tires. Keep in mind that is only for the increased diameter and does not account the increased rolling mass and road resistance typically associated with larger tires. You also mention the overall truck is heavier than stock because of mods. Also note that just because a gear calculator states a certain ratio it doesn't mean that ratio is even available.
If you have the factory option 4.10 gears than the calculator states 4.74 gears (actually available are typically 4.88).
Overall, between 37" tires, increased truck weight because of mods, and towing a 9,000 lb. trailer I would lean towards a 4.88 gear and possibly even 5.13.