郷愁 (kyōshū: nostalgia; homesickness) hometown + melancholy
The second kanji means “melancholy.” The kun-yomi form of 愁える is ureeru (a palindrome in romaji!), which means “to grieve.”
You may have noticed that “autumn” (秋, aki) sits atop a “heart” (心) in 愁. Is there a connection between autumn and melancholy? I thought winter was universally the most depressing month.
In fact, the 秋 in 愁 is a substitute for a non-Jōyō kanji that has the same on-yomi, 皺 (SHŪ, shiwa: wrinkles).
When you are troubled (that is, grieving), the brow furrows or wrinkles. So wrinkles + heart = to grieve.