My bf keeps calling his ex “sweetie and honey “?

My BF left a woman he was trying to be in a relationship with for me. He tells me how he complained to her about standing up to her family, stop letting them control her, how her family didn’t like him to begin with because he was older. his pet peeve was her not driving over/spending the night all because of her parents he said we were having sex and she still couldn’t stay over. he said he felt like she treated him like a friend and he wanted to feel like a boyfriend. A few months ago he told her “i met someone else and I’m trying to be with her” and she cried she started getting upset and fussing at him for meeting another girl. And she begged for him back but he told me he apologized and said “sorry sweetie l still be here for you”. I went through his phone. The day after he broke up with her though he texted her first saying “hey sweetie how are you doing” he initiated the conversation the next day after that too saying “hey sweetie how’s your day going so far” the week after he broke up with her she was still trying to see him and he was trying to clear his schedule to see her too from the text. weeks went by and neither one of them texted each other until last Month he texted her first asking how she was doing she didn’t reply. He checks in on her and calls her sweetie so, but why leave her only to continue to be sweet with her. He might have ended their relationship but he didn’t end contact and he jumped from her straight to me without any break