Whether or not you need a limited slip diff has nothing to do with the size of your wheels or tires - and by the way you still have not yet mentioned the diameter of your tires.Been thinking do i really need posi on 26s if im just driving it around?
With 3.42 or more rear axle gear, it's very easy to break the rear tires loose, even with unusually heavy wheels.
Do you NEED a limited slip diff? Technically, no.
Will you regret not getting one? Probably, unless you drive like Aunt Teak.