I am like the guy you are dating! I like texting quite a bit (family, friends, boyfriend.....) People who know me accept this, but also realise I don’t expect them to reply immediately, or text as much as me, and we will joke about it. (I always say, I’m one of those people who is shy at first, but when I decide I like someone and open up with them and come out of my shell, they will wish they could stuff me back in it!) It’s nothing sinister, honestly - I will just have something funny happen, or read something or see something or even think something that I think would be relevant or interesting to one of the people I like/love, and so I want to share it with them. My boyfriend, especially, we will joke about it as he isn’t a massive texter during the day, and I realise he doesn’t always even read everything I send! Luckily, my mom and a few of my friends text a lot, so I am never bored!
My brother is another who doesn’t text much, and is always moaning at me and my mom about how many messages there are on our family WhatsApp whenever he turns his phone on. We moan back at him about never having his phone on! But none of this is serious stuff, and no one is trying to infringe on anyone’s privacy - it’s all lighthearted.
Having said that I do try to be considerate and if he, or one of my friends, is clearly busy and not responding, then I do try not to bombard them with loads more texts..... But also I don’t operate a strict “no double texting” policy - after all, it’s up to an individual if and when they want to read their texts - it’s not like phoning someone 24/7 and demanding to speak with them then and there.......
I agree it is easier to make light of this in an established relationship - 7 weeks in is quite early days, and you don’t know necessarily if he is sensitive or easily offended - but could you maybe make a bit of a joke of it, which also communicates that it isn’t a sign of you being pissed off if you don’t reply for a while?
As long as you don’t feel he is texting to check up on you, I don’t think it is necessarily a red flag or even a sign of serious incompatibility - it could just be a small difference between you, of which there will no doubt be many (as is perfectly healthy).
However, if he reacts badly to the idea that you DON’T constantly want to be texting him back, then that would imply that he is controlling, rather than that he is just chatty with people he likes.....