Download and print a gauge and insure the cartridge is correctly set up & aligned.
Buy an inexpensive electronic scale (1/10 gram or less resolution) and refer to the cartridge's specifications for tracking force. There is no need to buy one sold for turntable use; they are all the same, essentially. $10 on eBay is fine.
Set the tracking force at least to the middle of the recommended range, and preferably higher. There is no danger of "wearing out records" with a high-ish tracking force, despite what most people assume. You want a tracking force that allows perfect playback under all conditions and with all LPs. Do not be afraid to use the highest recommended force ... it is, after all, recommended.
When a cartridge mis-tracks (most likely towards the inner grooves) due to insufficient tracking force, it violently oscillates in the groove. This causes permanent (and instant) damage to the LP and is the major cause of LP wear, not a reasonably high tracking force.
Be sure there is not something interfering with the un-encombered travel of the tonearm at record playing stylus height. Typical culprit here would be a tonearm lift arm (near the fulcrum, or pivot point of the tonearm, usually) that does not go to rest or is bent. Correct that problem if it exists.
Carefully remove the stylus (if it's removable) or install / move the stylus guard to a safe position, and check the free movement of the tonearm across the traversed area of the turntable platter.
Insure that the dust cover is not interfering with the rear of the tonearm as it traverses the record. Generally speaking you can play records with the dust cover up without issue; on some turntables the dust cover can create a chamber that causes feedback (on others it's OK to use it in the down position) but there is no real need to play records with the cover in place. Use it when the table is not in use.
I doubt that anti-skating is the problem, if it is there is something wrong with how it's configured. Try playing the record with no anti-skating and see what happens. It should work fine in that condition. There are those that consider anti-skating compensation to be completely unnecessary; there is also many cases where the anti-skating force is incorrect. Try using a lighter anti-skating force. Definitely too much anti-skating is not recommended.
With a hanging weight anti-skating mechanism, you adjust the anti-skating force by bending the rod that holds the weight.
The anti-skating compensation should definitely never move the tonearm toward either the spindle or the outside of the platter. It should allow the tonearm to stay in whatever position across the arc of it's travel without moving it in either direction, or only very slightly and slowly toward the outside of the platter (when the tonearm lift is not used, and the stylus is safely protected as per above). You could remove the platter for these tests if you like.
A note regarding LP length:
In order to encode the lowest frequency response in an LP groove, for most non-synthesized bass instruments, the total time per side must be limited to roughly 18 minutes maximum. A recording of deep bass (eg Bach Pipe Organ) would be less, perhaps 16 minutes or if a large pipe organ, which can go to 16 Hz, perhaps 14 minutes.
Any LP longer than that play time per side has been equalized in mastering to limit Low Frequency information. The maximum acceptable playback time for an LP containing music is about 24 minutes; with limited bass information. Voice-only records can be longer.
