Click on the note, look in the task pane, uncheck "use document font", click on font, on the right, under height, change the space
EDIT: As better men have noted, you can do this, but it has no effect. I stupidly tested it on a note, rather than a dimension.
I was going to say the same thing as Mike, except if you are trying to change the dimension text spacing rather than a note you will find the font button on the "Other" tab of the task pane. However I tried adjusting the space of dimension text from there and it seemed to have no effect. I think that is probably a bug.