If weight is your greatest concern, I suggest you go with "SL" (standard load) rated tires. Or if you feel the need for LT tires instead of P tires, go with a load range of "C." Fewer plies means less weight. Toyo makes the Open Country AT3 EV in SL and those paired with lighter wheels are very close to the stock weight.
@dubel mentioned these above paired with BBS wheels from the Tundra TRD Pro. It's the same setup I went with and it's working great. If you look enough on this forum, you'll see other users have done the same. But you have other options:
IMHO, if your use-case does not require any heavy towing or serious rock crawling, you really don't need tires with a heavy load rating. There's a bit of debate on whether or not more plies helps against puntures from thorns. If you're not driving offroad in areas with robust thorns, you don't even need to worry about it. With lighter wheels and tires, your mileage will be better and the ride will feel softer.
