Hi
If you change the preview resolution you change the VP preview window. For example if your clip is 16:9 and you change the preview to 4:3 then your clip is then resized to fit into the window but will remain 16:9 and you will have borders on all sides. On export and as there is now a clash .....clip 16:9 in a 4:3 frame you will have the choice of either Cropping the borders or resizing to fit.
Resizing will export the clip as seen in the preview with borders.
Cropping the borders will export the clip as 16:9 and consequently it will fill the screen but if borders or bars were present as part of the original clip they will still be there.
If you Resize to fit on export it will still have borders.
If you choose to Crop edges, the borders of the clip will be trimmed off and the clip enlarged to take up the space. As your image area is "fixed" so to speak in the clip this will also be enlarged with consequent loss of resolution.
However...
What I think you have -- it would be useful if you post an image from the raw clip so people could see it - - is a 16:9 clip with the image 480 x 270 in the centre of it. If this is the case, and its only a guess, it will inherently have borders or bars at each end as a matter of course
This is what I mean...

If this is the case then it is fairly easy to get your full screen image..
Add the clip to the timeline and click FX
Now select ROTATE and enter 270 for the rotation. Remember that the WHOLE frame will rotate with the black borders..NOT just the image section.
The sequence preview result in VP will be this....

There will be a border all around as the WHOLE clip was rotated . (See the example in the above post of my dog.)
Now you need to enlarge the image area...
Click the FX box and select ZOOM
Drag the sides of the box in to exactly outline the image.......

The sequence will now be full frame... As the image in this example is actually 480 x 720 which is not quite 16:9 the edges were dragged in manually, but you could ZOOM to exactly 16:9 by restraing the AR and lose a tiny bit of the frame to ensure the borders have been eliminated. The sequence preview is now a full screen image.........

The downside to this is the Zoom which enlarges the image to cut out the borders but lowers its resolution.....
Any other ideas would be welcome but I hope this helps.
Nat