Should I step back?

I’ve been talking to a guy on bumble since the start of December, he joked about not falling in love with him and I laughed. We met towards the end of December. We had sex but had a great d&m afterwards we then went out for dinner. A few days later I stayed the night at his. A week later, he said he wanted to meet again. I went over to his we had sex straight away and then chilled got food delivered and talked. I’m going away for a week and he said let’s meet next week and I said I’m away and he’s like “damn, when you get back maybe we can go to the tennis”. I don’t want to read too much into it but is this turning into more?

When I send a snap I don’t expect a reply from him but he does then we have a conversation that lasts a few days because we both take a while to respond. The conversation has finally ended, should I not snap him or message him? I feel like I’m coming across as annoying and I don’t want to be. Should I wait for him to reach out maybe?