Welcome to BF and congratulations on the decision to improve your health/fitness! Cycling is such a great hobby.

I started with a similar situation as your's (height/weight/BP/back issues). For me, the weak back was a lack of core strength. Back issues are no doubt tricky and somewhat unique for each of us. I started, very slowly, doing planks and can now do 100 mile rides on my road bike without back issues.

Enjoy your ride!