I found a complete working solution elsewhere; I am posting it here to help anyone who has the same problem.
Word 2007 physically locks that font size box so that typing a number in one field instantly overwrites the other. The software simply will not allow two different font sizes to exist in that menu.
Because Word forces them to match, the only way to get 12pt Western text and 14pt Asian text is to bypass the Font dialog entirely using the workaround below. (I have just tested this and it works perfectly.)
If your document is already typed out and both fonts are stuck at size 12, you can use Word's advanced Find and Replace to target only the Asian text and boost it to 14 without touching your Western text.
1. Press Ctrl + H to open the Find and Replace window.
2. Click the More >> button at the bottom left to reveal advanced options.
3. Click inside the Find what box at the top.
4. Look at the very bottom of the window, click the Format button, and select Language.
5. Select your specific East Asian language (e.g., Chinese, Japanese, or Korean) and click OK.
o (You will see "Language: [Your Asian Language]" appear right under the Find what box).
6. Leave the Find what text box completely blank.
7. Click inside the Replace with box and leave the text completely blank as well.
8. Click the Format button at the bottom again, but this time select Font.
9. In the size box, type or select 14, then click OK.
10. Click Replace All. Word will scan the document and instantly resize only the Asian characters to 14pt.