I can only judge from pictures, but your Walkman looks similar to a EX-1 mechanism, of which I use 70mm square cut belts (at least that's what it said on the packet at the shop, can't remember if it was 0.7 or 0.8mm thickness). It should not be very tight.

One place to check is for any traces of the old belt left stuck on the flywheels and pulleys.

Just how tight is the new belt that you have fitted? An overly tight belt will in time wear out your gears and pulley wheels.

The wow and flutter you mention are more likely to do with contamination on the pulley wheels where the belt travels on, especially if the previously belt was a gooey mess. You make no mention of having previously cleaning the belt path prior to fitting the belt or what state the original belt was in.

What about the capstan and pinch roller? Are they clean? Is the pinch roller perfectly round? If there is a dent in the pinch roller this can cause sound issues too. Check also to see that none of the tape path guides are broken or missing, as this can lead to loss of tape path stability.

If you open the cassette door and look inside you will see a black round rubberised wheel. That is the pinch roller. The metal pin opposite the pinch roller is the capstan. If you have an auto reverse unit, it will have two sets.

Both pinch roller and capstan should be clean for good audio reproduction. Use denatured ethanol on a cotton swab to clean them both of the oxide dust that is usually shed from tapes and adhering there. If after cleaning the pinch roller, it is still shiny then chances are the rubber on the pinch roller has dried out and it will have to be replaced. Also if there are any dents on the pinch roller, it will also have to be replaced since the dents will affect playback quality.

Whilst cleaning them, you may also want to clean the magnetic head preferably before cleaning the pinch roller and capstan if using the same cotton swab. The magnetic head is the shiny metal piece in the middle. Clean it along the direction of the tape travel to minimise causing any scratches.

Inside the tape compartment, right beside the heads, you should see 2 little rubber wheels and 2 metal shafts. The rubber wheels are pinch rollers and the shaft is the capstan. Pinch rollers should not have any deformations on them, otherwise there will be wow and flutter.