16mo, currently in process of moving to cot rather than co-sleeping.
I'm afraid I do pick him up, breastfeed him and put him back in once he's fully asleep because that is what works! It's a bit of a pain but I'm intending to night wean as soon as he's used to the new routine of starting night in cot.
I will do what I did for DS2. Give myself a time limit - currently if he wakes up and it's past 1am I bring him into our bed. Or if he wakes less than 1 hour after the previous wake up, or if I have had 2x failed attempts to put him down.
I will increase that time - I think 2am probably starting tonight. Once 2am is standard increase to 3am etc. And with the less than 1 hour wake up I might get stricter with myself and make the rule 2x gaps shorter than 1h.
In addition to that, add in a delay before going to get him. First of all when he cries just listen for a minute or two, in case it's a dream or a fart. If crying continues, go for a wee (to add more delay and also in case I'm stuck there a while) - with DS2, I would often find that by the time I'd done a wee he had gone back to sleep. DS3 I'm still responding to immediately at the slightest hint of noise, because he's sharing with DS2 and because I want to build up the cot as a safe place at night not somewhere he dreads going into. But I will start the delay once he's a bit more used to sleeping there.
Then a delay once actually in the room as well. I have a smart watch with a lit screen so I check the time when I open the door and do everything in slow motion - walk slowly to cot, pick him up slowly, walk the long way to the chair, sit down, get comfy, get him in position, open clothing all slowly, so that it's 5 mins from door to boob. I will then increase this on subsequent nights. You're supposed to increase to 10 minutes but I think I will be a wimp and do 7 
As a third step I'll add in cutting him off before he is quite asleep. If I'm lucky/time it right then I can just rock or hold for the rest of the falling asleep process. If I time it wrong and he protests too much then I just relatch - but this gets easier and less sensitive the more I do it.
Some combination of the above 3 got DS2 to sleep through. He was over 2, though. Previously at 18 months with DS1 and DS2 I was just feeding them overnight as much as they wanted basically. I'm trying the night weaning a bit earlier this time because I have come to realise that they don't do it magically by themselves, much as I would wish! But it feels exactly the same as when I did it with DS2, so I don't see any reason to wait and am hoping it will be successful.
All three of them have had periods of long, quite intense wakes at night at this age - I think it must be a developmental thing because it seems to precede a spike in language acquisition or walking or some kind of skill that they seem driven to practice, like putting things in and out of other things, or handling tiny objects, or building towers or doing those wooden jigsaws (shape matching) etc. DS2 was the worst for it and did it for weeks at a time basically every night. Also pre-molars and canines can be coming through which is disruptive, and if he's in childcare then it might be illness/viruses as well. Growth spurts leading to excess hunger too.