If baby is happy to keep nursing then let him, if he is waking up because you have put him down in his cot then try keeping him with you, he may sleep better that way.
Have a look at this as these will tell you everything you need to know about bfing and milk supply.
In a nutshell though:-
The more baby nurses the more milk you will make,
the shorter the gaps between the feeds the more milk you will make,
breasts are never 'empty', there is always milk even if it isn't in massive amounts (then breast compressions are your friend if baby is fussing),
the 'emptier' the breast the quicker the milk is made and the fattier it is,
breast milk contains a substance called FIL, the more FIL there is in the breast the less milk made (FIL switches off milk production cells while it is in the milk cell and turns it back on when it leaves when baby drinks).
Surprisingly giving formula isn't going to increase the amount of milk you make, it may temporarily make it look like there is more milk as the gap between feeds is artificially increased leading to engorgement/over fullness. That is an illusion though as behind the scenes the breasts are slowing down on how much milk they make (see point about FIL) rather like a stop-cock valve as otherwise you would have exploding breasts. If you keep leaving long gaps your breasts get the hint and drop back on production which would mean a lot of work to get production back up to speed.
HTH helps and you get some rest with baby.