Resizing a video file recorded with quicktime

If only part of the screen is of issue then use MPEG Streamclip (free) , set the export (to MPEG-4 and select an iTunes preset like iPod or iPhone) to the same size as your screen (1900 X1200 etc.), then use crop, which is a bit of a hit or miss proposition to crop left, right, top, bottom to save and export just the part you want to see.

There is an export preview in Streamclip so you can see in seconds what you are going to get and estimating the cropping points is not that hard, as you know how big the screen is and if you want 1/3 in the middle you set left and right crop to be 1/3 of the width each.

Note the end result is scaled down to the crop settings so it is not 1900X1200 using this example, it might be 600X400 etc. Just the part you want, life size.

"Export" using QuickTime Pro or "Share" using X to reduce the file dimensions.
Smaller dimensions equals smaller file size but your screen capture may be difficult to view.