I've just pulled this from the the NHS website:
You are seriously overweight for your height
Your BMI is 32.5
If your BMI is between 30 and 39.9 you're obese. This means you're well over the ideal weight for your height. This could cause serious health problems and affect your life expectancy.
Are you eating more than the recommended amount of calories per day? Are you getting enough exercise? Once you gain the confidence to start exercising regularly you'll notice a huge difference.
Speak with your GP for advice if you've tried to lose weight without success.
Top tip
As part of a healthy well-balanced diet, cut down on salt and alcohol. Try to eat more fresh fruit and vegetables. Also, eat smaller portions at mealtimes and avoid snacking between meals. I don't mean to sound offensive. This is their words not mine!
It really depends on what that weight consists of. I know rugby players that weigh that and most of it is muscle. They eat a very balanced diet and consume plenty of calories but do plenty of exercise to burn it off. In that sense 17 stone is 'healthy'
If your weight is mainly fat, then I would put in a strict cardio-vascular and weight loss / fat burning exercise plan into place. Combine that with a low carb / fat (little bread, pasta and potatoes, chocolate, cream) but high protein (fish and nuts etc) diet and you should loose a couple of stone in a matter of months. Depending upon how well you keep to the diet and how much exercise you do. I would recommend a trip to the gym 5 times a week.
I would personally run / jog for 20 mins, do an energetic sweat producing bike ride for 30 mins and finish off with some rowing for a futher 15 - 20 mins. The key to weight loss for me is to exercise that's over a longer period of time to a pace that you can sustain.
Don't blitz it for 5 minutes where you're completely exhausted aftwards.
I don't know what the CAA medical requirements are for the BMI so can't give you an exact answer to if you should wait or not. If you got down to about 15 stone then you should be ok. Best check with them before going to any medical I would say.
Then you know what you need to do and where to get too.
Good luck.