| I cycle off road, and do free weights to build leg power and core muscles, and a bit of toning for upper body. I've played around with insulin, taking carbs and my routine to get something that works with the diabetes.
I'm assuming you understand why you went high during - the liver dumps glucose into the blood stream in response to high intensity exertion (technically once you reach the lactate zone typically above 140 bpm)
I assume you test before during and after your program to see how things are going.
I have some suggestions...
1) lower the intensity of the weights program. Go for endurance (15+ reps) rather than power (<6 reps). This will help you stay below the lactate threshold and prevent an extreme BG rise.
2) take a correction shot of insulin - If your weights program continues to raise BG then you could consider taking insulin as you start your program (definitely need to test this one, and err on the side of caution) - alternatively you can still correct at the end of the session.
the low afterwards is caused by the muscles becoming more sensitive to insulin, and so absorbing glucose. The effect typically lasts around 24 hours, sometimes a bit longer.
suggestions...
1) try dropping your basal dose - if you are on MDI then just dropping your basal by 2 units may be enough to take the edge of the lows.
2) drop your carb ratios at meal times (if you are using them)
3) have small regular snacks to keep your BG up - and consider a before bed snack to keep BG up overnight.
I got to my program by experimenting. You will have to do the same - sometimes you will get it wrong. Don't worry about it give yourself a correction shot or take some sugar, and figure how you are going to manage it better next time.  | 
