Maybe you're taking the water away too early and he's thirsty? When Zoe was 12 weeks she needed water until bedtime around 9pm and I'd let her out around 11pm and then she'd sleep until morning. If I noticed she didn't drink a lot of water she would always wake up crying in the middle of the night and run right to her water bowl.
We also used a larger wire crate with a blanket over the top of it. If he's doing okay making it out to potty then maybe he's ready for more room?
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