Waking up in the night and size are NOTHING to do with a baby being ready to wean.
It's really common for a baby to wake up in the night at this age. Actually, their waking habits change all the time in the first year but at 4 and 5 months they go through lots of changes (rolling/sitting etc) and it always affects their sleep.
And people are as likely to say 'ooh that baby's small, wean him' as they are 'that baby is big, wean her'. It's meaningless and in fact if your baby is large and has remained so, it's a good indication that milk alone has caused them to thrive. Certainly there are more calories in milk than in any other food you could offer a baby under 6 months so if your baby is 'hungry' they need more milk, not less. Up to 12 months their diet should be mainly milk anyway.
Babies need only milk for the first 26 weeks. Around this time they will show developmental readiness for solids. Readiness is actually about when their guts have matured to be able to cope with solids and nothing to do with watching you eat, increasing feeds etc. Babies watch you do everything. In fact a newborn can mimic mouth movements/tongue movements, it's just the way they interact with their carers.
Obviously, some babies will be ready before 26 weeks and the signs that they are ready are...
Able to sit up unaided
Loss of tongue thrust reflex
Ability to pick up food, put it in their mouths, chew and swallow
To this end, if you stick baby friendly chunks of veg in front of them while they're sitting up and they pick it up and eat it, they are displaying the external signs of readiness and theoretically you can assume their gut has matured to the point it needs to.
If I were you I'd offer milk to requirement and let the baby join you at mealtimes. When they're ready, they'll help themselves, answering the question for you.
It's hard when they wake up again having slept well but it's normal for them and they will do it again in the first year, just as you're starting to feel human again. 