Should I give him another chance?

I've known this man for a year now. We somewhat dated for 6 months, and broke up b/c he was a commitment-phobe & I caught him in stupid lies. We didn't speak for a month after that, & for the past 5 mo., we have been just casually seeing eachother/FWB. At first, it was purely just physical and us just having fun, but lately, he has been asking me where I'm going, who I'm going with, & jokes around if there are any other men. When I was sick, he messaged me all day asking if I was ok, and kept offering to get me food/meds. When I sleep over, I wake up to him cuddling with me in the middle of the night. It just seems like he's starting to treat me like how he used to when we dated, rather than just someone he's fwb with. Yesterday, I went on a limb and sent him a good morning text stating, "I woke up this morning and thought of you...I wanted you! lol. Hurry up and come home!" & to my surprise, he wrote back, "thats funny, b/c I woke up thinking of you too."