Stearing Wheel Shake at Low Speeds

Hey, I have a lifted 99 jeep Cherokee that just recently started to get this really bad shake in the steering wheel, Like the steering wheel jumps about an 2 inches up and down. This only happens at speeds from 15-25 mph during acceleration but when i let off the gas it immediately goes away.
The things i have checked and replaced are: Both wheel bearings, Rebalanced tires, took off front drive shaft and drove it and still has problem, steering is all tight and greased. I don't even know where to look anymore. Someone please give me some advice on where to check. Thank you everyone.

Up and down as in vertical?

I would check the mounting bolts of the steering gear box first.

get a new steering stabilizer if yours is stock. *** get one and put it on yourself.

Yes vertical. My steering stabilizer is about a year old. Think they got out that fast? Its a RE.

If the movement is vertical and under torque, I would look elsewhere.

If the steering box mounting and frame are Ok, check the motor under torque--have a friend put it in gear, stand on the brakes and rev it up--don't stand in front of it. See if the motor is jumping in its mounts and hitting the steering somewhere.

I don't think the stabilizer would go bad in a year, and I don't think if it did it would give you vertical movement. However, try disconnecting the stabilizer and see if that makes a difference.

If its not stock I'd say the stabilizer isnt the issue. Perhaps put it up on stands and try to see if you have anything that might be loose.

Just got done from looking at it. Putting a load on it while breaking is causing the passenger side axle to bind backwards.

Take a look at you upper and lower control arms and their mounts.