I think being "sleepy" is now the norm. Pictured here are 2 of the resident sleepy heads in my household. I, too, am perpetually sleepy.
Hanaa is now a day away from reaching 4 months. Her sleeping hours have grown up to 6 hours at a stretch between 0000 hrs to 0800 hrs. The correlation between baby's increase in hours and her parent's sleepy head condition is: the longer baby sleeps at a stretch at night, the less sleepy her mommy and daddy are.
I heard from some parents that as their babies progressed from newborn to 1yr old, their babies' sleep durations are increasingly short per nap in the night. I'm surprised to hear this as my baby seems to be on the opposite track. Based on Hanaa's great mood in the mornings, I believe she's doing just fine.