Make sure your Preview screen, Movie project, source data, and output options are all set to the same aspect ratio.
If your source data has mixed aspect ratios, both 4:3 and 16:9, then I don't think you are going to be able to get rid of the borders without distortion or having to enlarge so much that you lose a lot of the picture.
If you have mixed aspect ratios in your source, then determine which you are going to use for output and set the preview screen and Movie properties to that aspect ratio.
You don't say what version of MEP you have. In MEP 16+ you can adjust size and position in Effects > Movement effects > Size Position.