Baby drinking more at night than at day

My baby is 9 weeks old and during 6 first weeks he used to drink more at daytime than at nighttime. After he got his first vaccine, his drinking changed from drinking more at daytime to drinking more at nighttime. He drinks twice as much at night.

I’ve tried to give him less at night so he would drink at day, but then he just woke up more often.

Do you guys have any suggestions on how to change this? Or do I just have to wait until it changes by itself?