First, I would check if the half-loading arm is sticking.
Located in front of the take-up (right hand) reel table, usually a thin metal post on a sprung swinging arm.
This arm pulls the tape against the audio/control head.
Occasionally they may stick if the lubricating grease has gone hard. It should move easily toward the capstan and spring back again on unload. Watch it's action during loading/unloading of a cassette.
A small squirt of some tape head cleaning fluid will normally free it if it's sticking. Don't use any undue force on it, as it is critically aligned for smooth tape transport.
Otherwise, the problem may be due to the extra tape tension in the mechanism. At the beginning of the tape there is a heavier load on the supply reel table. If this is the case then there are many possible reasons the video is struggling, but often that's due to a worn cylinder surface, causing drag on the tape.
Cobweb, October 2006