Rita Ora Travis Barker Is Really ... Rubbing Off On Me

10/5/2015 10:00 AM PDT

Rita Ora -- Travis Barker's Really Rubbing Off On Me (PHOTO)

Two weeks in and Rita Ora and Travis Barker are already acting like they've been living together for years. 

The new couple rolled out of bed Sunday for brunch in West Hollywood, and it looks like she went shopping ... in his closet. Barker's grungier style is clearly rubbing off on the "Black Widow" singer, who usually opts for less cover up.

As we told you, they've been inseparable since first hooking up at a charity basketball event last month ... she's even been staying at his West L.A. home every night.  

They say the couple that dresses together ... spends less on clothing. That's all.