Change the cartridge.

Or if an older home change the bib washers.

Who told you it was hard water? It's a leaking cartridge.

Thanks, everyone. Home is only 14 years old. I had a hard time removing the base of the faucet handle because the nut was way too tight. Surprisingly, I was able to get it off by tightening it a little first which loosened it in the other direction too. Anyhow, it's a Moen and I couldn't get the plastic retainer off using needle nose pliers. Turns out there's a special tool for Moen which I'll pick up when I get the cartridge. Everyone, thanks for the help in pointing me in the right direction!