Tonearm and Anti Skate Question

Hi, I have a question regarding the behavior of the tonearm on my Pro-ject Classic turntable.

Whenever I use the lifter to raise or lower the tonearm to/from the record, it always swings towards the outer edge of the record for a distance of about 1/2 inch to 1 inch. I have checked the level of my turntable with a leveler, and I have set the anti-skate setting based on the recommendation from the user manual. Sometimes when after playing the last song on the album, as the tonearm moves into the "no groove" zone near the center of the record, the tonearm gets pulled back and played the last few seconds of the record over and over.

I have tried all 3 settings of the anti skate and it still behaves the same. I finally removed the anti skate weight, and now the tonearm doesn’t swing out anymore. I can’t seem to hear any difference in sound quality at any anti skate settings or without anti skating at all.

Anyway, the question I have is whether anyone know what might be causing this tonearm behavior, and whether it is ok to run the turntable without any anti-skating setup. Will this damage my record if I do so?

Thanks in advance.