I probably should have looked up their respective ages. I suppose that Burke was younger than Freeman was at the time that they each played Watson, but Burke acted older or maybe that's just the effect of period costumes. In A STUDY IN SCARLET, Watson has recently been in Afghanistan with the army and I'd expect he was a young man at the time (around thirty) and the adventures require him and Holmes to do a lot of physical things.
I don't see him as the old fusspot that some versions present (even though I like both Nigel Bruce and James Mason in that role). Given Watson is still alive and well during WWI, he ought to be young enough circa 1887 to get through the next thirty years in good health. I could be wrong, I'm no Holmes expert, but that's the mindset I have when I'm reading the stories.