I'm nearly 57, and have only really started taking on big hills/mountains in the last few years. I guess I'm probably much heavier than you (as I'm taller and heavier that the vast majority of people), so I totally get your concerns about overdoing it. I have done pretty much what
@ianrauk and some of the others above have mentioned, and just sat back and enjoyed the hills at my own pace. I've opted for a bike with a granny ring on the front and a dinner plate of a 34T cassette at the back, and I just pace myself steadily.
Whenever my breathing seems to be getting out of control, I ease right off in the lowest gear I've got .... or even stop for a breather if absolutely necessary. On club rides, when we hit the big hills, I'm usually about the 8th or 9th man up out of 10 of us, but who cares? And a couple of others will have either put a foot down or taken the walk of shame at some point. I once took the opportunity to check out what deep, steady breathing does for you physiologically while using a gym bike, and it is remarkable how it can keep your heart rate under control. Of all the techniques I have used for surviving the hills, I think consciously keeping control of your breathing and easing off on the pedals when necessary is the best advice I can give you.