Slipping is just not the right word for it. It is not your transmission or Torque converter. It is a lack of power on take off you are describing near as I can tell.
Your year, 87-90 is notorious for weak grounds causing many problems, including yours, easy free fix..... Grounds that the engine computer sensor depends on for accurate data and ability to deliver power and acceleration.
You test and locate and fix any bad ground connections between the sensors and the battery negative post first.
The TPS may be worn out and causing your problem. Test it after the grounds are verified or fixed.
The Vacuum line from/to the MAP sensor may be just a little loose at the throttle body connection or damaged and leaking vacuum in between. It must air tight!!!!! Super sensitive.
O2 sensor heater may not be working at idle (Sensor or damaged wiring or bad O2 sensor relay..) and thus does not work right on take off from a stop.
I have 4 renix (87-90) Cherokee jeeps I have had for 6-13 years now and I have never fixed this problem, even, with a new
IAC Idle air controller.
It has always been a bad ground, TPS, MAP sensor vacuum line leak, or ignition stuff like fouled/worn plugs, bad Distributor, bad Dizzy cap and rotor or dying spark computer, ICM, under the HV coil. A bad IAC will not cause hesitation when you stomp on the gas pedal!!!
All of these can be tested with out spending a dime, by using a volt meter, DVM to test the sensors and wiring.
Best right ups, step by step for testing these is on cruiser54 's web site. Nice neatly organized!!!!
http://cruiser54.com/
Low fuel pressure, lack of flow is also a possible issue, but at this point it is at the bottom of the list.
A
bad ground is very common!!!
A leaking vacuum line the MAP #2.
A
bad TPS or
TPS ground third and almost a tie with #2.
And not far behind 2 and 3 is a
weak spark from the ICM to the Dizzy parts the plugs.
Hypoid and Lawsoncl know these rigs well too.