[kendawwwg]

you didn't say long bed or short,, long bed helps, short beds tend to wag, it has to be in your load leveler adjustment
getting a good weight distribution hitch ,with sway control like the e2 by fast way, might help
i tow a 25 foot 8 foot wide travel trailer at 5200 lb , it tows like nothing is behind me, so smooth, no sway
granted i have the diesel motor, in a long bed, but rear suspension should be same.
get your front and rear fender ground measurements before you load trailer, then load trailer with weight distribution hitch engaged add or remove washers, until you get front end measurement number to match your unload number,do not use hitch to lift rear end sag,, just get front end number as close as you can to were you started unloaded