The ::cue pseudo-element can contain "the properties corresponding to the font shorthand" (spec). This includes font-size.
Lack of support for this was flagged in #8958
Implementing this probably involves editing the WebVTT CssParser. WebvttCssStyle already has font size support (though it doesn't seem to be used, and I'm not sure it ever has been), so it should be possible to re-use that.