Oh those night feed changes - just when you think you know where you are it all becomes different :(
Expressing is no indicator of supply at all and changes to the amount that you can express is not only normal, but good, because it is an indication that your body (as it should be at 8-9 weeks) is settling into making just the right amount of milk for your baby and not too much (oversupply is a real problem in itself so this is good).
How often are you feeding during the day? Has anything changes to your daytime routine? What happens during the night feeds? Does he feed until he's sleepy or asleep and drops off himself? Can you offer the other breast? Where does he then go to sleep afterwards?
Formula feeding to get them to sleep longer assumes a) that you don't have enough milk (almost certainly not the case as you've got this far unless you are limiting feeds elsewhere, in which case introducing formula will further undermine your supply) and b) that he's JUST hungry as opposed to maybe hungry and possibly also cold/hot, wanting a nappy change, or just (most likely) wanting to be close and cuddled to you which is what I'm wondering as you're struggling to get him to sleep.
The evidence shows that giving a bottle of formula doesn't make them sleep longer (although it might). The upside to doing it is that it might. The downsides are:
- One bottle of formula a day will remove the protection that breastmilk gives to the lining of the gut, making him more prone to allergies and gastroenteritis
- It will impact your milk supply because your body will make that one bottle of formula less each day
- Exclusively breastfed babies are at a significantly reduced risk of SIDS and we are not sure how mixed feeding affects this. One part of reducing the risk, though, is that babies are not designed to sleep long periods of time between birth and around 6 months because their systems are sometimes too immature to kick-start themselves if they go into too deep a sleep and their breathing is affected. This is partly why SAFE bedsharing or room sharing has a protective effect because the mother's breathing an heartbeat next to the baby (the latter when bedsharing) seems to be a "trigger" for the baby to breath if affected like this.
I must very strongly stress that the latter reason sounds terrifying, and SIDS IS terrifying - but it must be put into the context of how exceptionally rare SIDS is, and balanced with the fact that if you are completely sleep deprived you are not necessarily in the safest position to, say, drive the next day. I'm just trying to put across info so you can try to work out what is best for you.
So. I would consider trying to work out why he's waking first of all. He's probably hungry - can you fit any more day feeds in at all? Is he getting everything he needs when he wakes (ie boob until he falls off - next one if he wants it - offer the first again if required). Can you snooze while feeding by setting up a safe bedsharing space and feeding lying down? Would bedsharing be an option for you if he slept better with you?