Sounds like the tires have balancing beads in them. 35" tires should balance with regular wheel weights. Will probably want to get them rebalanced and do the chalk test to find the right psi for your Jeep.
Can you post pictures of your suspension? That would give us a better idea of what you have and don't have.
But from just reading your descriptions, it sounds like you will want to invest in front lower control arms, rear upper control arms and front and rear adjustable track bars to get your suspension back in line. These parts will make a night and day difference in the drivability.