I have 2000 tacoma 2.4 and 32s. I was wondering why it shakes from side to side pretty violently when I go over 70mph.  

I had a 1995 Tacoma V6 with 34x9.5's it done the same thing at around 60mph. Had the tires balanced 3x's. This was a brand new truck at the time, to no avail i had to go with smaller tires. Someone told me i needed to have them balanced by shaving the tires? Every tire shop i went too looked at me like i was crazy! So i downsized.  

yep, it's refered to as "cutting". you can probably get it done at a tire center that sells tires for tractor/trailers. another thing to consider....your steering stabilizer. mabe go with a double set-up.  

i had sorta the same problem with my new tires on my 93 k1500. the truck would sway all over the road almost getting in an accident a couple times.turned out the sidewall was a 10 ply and not an 8 ply and the tire shop had the pressure to the max at 80psi.so i aired down to 55 psi and the problem went away. i guess make sure what ply you have cause that might be one reason for your swaying and shaking.