S.H.
He may be going through a growth spurt.
Typically, a growth spurt occurs at 3 months.
He is probably "needing" to "cluster feed"... which means a baby needs to feed even every hour.
Breastfeeding is hard work... but for a baby, they need to feed.
Cluster feeding, usually occurs when a baby is having growth spurts and developing a lot, and going through lots of growth changes and/or hitting milestones.
Is he latching on properly? Is your milk supply adequate? If not, a baby will always be 'hungry' and wakes up a lot. And, some babies just have ginormous appetites, which coincides with their growing.
I would make sure you are producing enough milk, stay hydrated and drink lots of water. When a baby starts to need to feed a lot, it usually then triggers the Mommy's body to produce more milk. Its nature. Its for a reason.
30-40 minute 'naps' is not much... often times a baby will 'stir' and toss and turn or 'seem' to wake... but it does not mean they are "done" with their nap. Try waiting... then if he really calls/cries for you, then pick him up and/or feed him. If he is still seeming to be tired....then he probably needs more sleep, or that his sleep was disturbed.
But, babies wake, and they feed. Its what they do. 24/7. Feed on demand, always.
Try asking your Pediatrician too.
I think he's hungry. But ask your Pediatrician...
If you are going to wean him... I would not do it at growth spurt periods... because they need more intake at these times, and they need you. And, ask your Pediatrician about "how" to wean him and start him on Formula, if that is what you really want to do.
All the best,
Susan