I think I understand the issue here, but it isn't a simple fix. The basic issue is that each page of the document is 4.25 inches wide by 5.5 inches high. This page size is 1/4 a sheet of letter paper, not half. This size would be ideal if the paper was folded into fourths, but the booklet printing folds it into halves.
As a result, when acrobat rotates the pages to make them a booklet, the program resizes each page to keep it proportionate. to accomplish this, and leave a gutter to fold, means that the final size doesn't fill the half page, leaving a large margin.
The cleanest way to fix this would be for each page to be 5.5 wide by 8.5 high, but that's not the proportions of the existing pages, so that would require remaking the entire document in the new size.