6 week old babies can tire really quickly - I wouldn't worry too much about "keeping" DS awake - focus more on the tired cues (you need to figure out what they are as all babies have different signs) and making sure you put him down when he needs it. My DS is 5.5 months and still sleeps a lot - so much so that I have posted twice on bellybelly worrying about how much he sleeps and also called the MCHN once about it. No one but me was worried - some babies need a lot of sleep and I've been told to enjoy it while it lasts.

When he was little and awake we tried to really engage with him - like the suggestions above - I'd also hold him and bring him outside and describe what he was seeing - also, tummy time - and just sitting with him and cuddling and talking to him, making silly faces, twinkling my fingers around his head so he'd eye track, kiss him and tell him where I was kissing him, and dance for him so he can watch (kind of how I get my cardio and he loves it), read really short books, look at family photos and talk about who everyone is, etc (and no way did I fit all these things in during any single awake period - 1 or 2 activities per awake period was enough). Often he would start showing tired signs after 30 minutes and this was even more true right after his "longer" night sleep.