The couple were photographed together for the first time last Thursday jetting out of the U.K. but stayed incognito wearing matching hoodies pulled over their heads.
They later touched down in Los Angeles and reportedly headed to the Grammy winner’s Beverly Hills home before flying to Nashville over the weekend, where they were pictured on Swift’s apartment balcony.
“Taylor and Joe arrived in Nashville on Friday and spent the weekend there,” a source tells PEOPLE. “It does seem they’re getting more serious. They had a great weekend together.”
Last month, multiple sources told PEOPLE the “Shake It Off” singer is purposely keeping her new relationship under wraps after “learning from the past.”
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“Taylor has been insanely private about her relationship with Joe,” said the source. “She wanted to get to know him without any chaos.”
Swift, 27, has been reportedly donning disguises while renting a house in North London to spend time with Alwyn, 26, who’s “a very normal, down-to-earth guy,” said another insider. “He’s private and low-key.”
The singer and the actor are longtime friends and Swift was first spotted publicly with Alwyn last fall after attending a Kings of Leon concert with a group of her pals.