You let him take care of BB for a week, see if he feel tired too.
I think your C6 is not ready for being a father, BB is not only belongs to you, he is also need to take some responsibilities. Sounds you don't have maid, right? Anyone can share the housework or take care of BB?
Tell him how you feel and made him understand the situation.
教 養 孩 童 , 使 他 走 當 行 的 道 , 就 是 到 老 他 也 不 偏 離 。 (箴22:6)
Train up a child in the way he should go: and when he is old, he will not depart from it. (Proverbs 22:6)