If you want help with the iWeb method of playing video, you would need to publish the URL to the problem page.
This way of playing movies is very outdated and requires the visitor to have the plugin installed in their browser. Many windows user don't.
The video file format should ideally be an MP4 and the video format H.264 optimized for streaming so that the movie will start to play before it is fully downloaded in the browser.
Autoplay should never be used and its far better to load a poster image and prevent the movie from playing until the visitor selects it. Otherwise the page download time will be effected and the movie will stutter and stop as appears to be happening in your case.
If you want to depend on the QuickTime plugin you should consider using a code like those shown on this page...
http://www.iwebformusicians.com/Website-Movie-Video/Poster-Movie.html
The second method is better if you think some visitors may be using mobile devices.
Nowadays its more usual to employ HTML5 playback with flash fallback for outdated browsers. VideoJS is probably the easiest solution when you only have one video per page...
http://www.iwebformusicians.com/Website-Movie-Video/Fallback-To-Flash.html
A poster image loads with the web page and the movie file is prevented from loading by setting preload="none" in the video tag.
Using this method you can get away with uploading only an MP4 (rather than mp4, ogg and WebM) since the player will fallback to flash for Firefox and older versions of IE.
Flowplayer is a better bet when you have more than one movie per page since it can be set to stop one movie when another is selected...
http://www.iwebformusicians.com/Website-Movie-Video/Flow-Player-5-2.html