Letters in small caps (\scshape) are larger (height and width) than lower case letters. How can you make them the same size?
Minimal example:
\documentclass{article}
\begin{document}
Default: \textsc{a}a, \textsc{b}b, \textsc{c}c \dots
Solution should look more like this: \textsc{\footnotesize a}a,
\textsc{\footnotesize b}b, \textsc{\footnotesize c}c \dots
\end{document}

scshapefor theorem headings, and I don't want the size of the lower case letters to change in the middle of a paragraph. – Randy Randerson Feb 07 '16 at 22:12fontspec. But why not use a font designed in such a way that the small caps are to your liking. 'Faking' font sizes usually looks obvious and not in a good way. – jon Feb 07 '16 at 22:50fontinstdoes not match fake small-caps to the size of loawercase. (I think it uses 80% of uppercase height, but might be misremembering.) – cfr Feb 08 '16 at 02:12