I have been working on some spec sheets and, ideally, would like the text size larger to improve readability. When creating text, changing the size is as easy as editing the text and changing the size. With a dimension, however, that method doesn't work. Is there an easy way to change a dimension's text size without having to make a change in the styles??
I know you were trying to do this without messing with styles, but it sounds to me like that is exactly what you should do anyway.
Create a new dimension style for "Spec Sheet Dims" and a corresponding text style if needed, then you'll have it available for future spec sheets. Even if it was possible, opening each dimension and manually changing the text size would be a lot more work than just changing the dimension style would be.