The couple was spotted holding hands while strolling the street in Los Angeles, reported Ace Showbiz.
The pair wore matching plaid shirts, training pants and sneakers.
They tried to avoid any attention with their low-key look and by hiding their faces behind sunglasses.
"They have been dating since last summer," a representative for Weber said.
Weil, 40, and Weber reportedly got close after their respective divorces last spring.
Weil was previously married to actor Paul Adelstein from 2009 until 2016. They share a daughter together, 7-year-old Josephine.
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