My sincere condolences.
About your D&D situation (which isn't really morbid - just perfectly normal displacement activity):
I could see not playing on, honouring his wish forever. On the other hand, I doubt he meant it like this, and would probably have wanted you to carry on without him - in life as in D&D. I say go with what you feel is the right way. Nothing we say can decide this for you.
Besides that, playing on might be a good or a bad idea, depending on how you'd deal with moments like "if Jessie were here, he'd just have charged in, with none of this diplomatting". It could be a way to remember a lost one fondly, or it could rip open wounds. Again, you must know this for yourself.
What I agree on, though, is that if you play on, his character should get a proper place forever after. The D&D equivalent of a candle in front of a picture of him. This you might want to do even if you decide not to play that campaign again.