My 2nd was back-to-back and weighed 9lb 1oz, decent enough size for me!
I did go into labour after my first sweep, so have no experience of induction....
But at this stage you're so close to 42 weeks you need to just go with your heart. Do you want baby to arrive ASAP, or in his own sweet time? I think in your situation I'd go for an induction just to speed things along and also for your own sanity as you're in pain and waiting.
I can reassure you I think - DC1 back to back 9lb 8oz - 25 hr labour - 42 weeks. Dc2 induced at nearly 42 weeks but only took the pessary to start things - done in 3 hrs total! 9lb 1oz so not small but had been told he would be 10lb. I would book am induction if poss for near 42 and then see if he comes before but I assure you it will be faster and easier (but pretty intense!)
My dc3 was 9 days late. back to back and induced. She was a pound bigger than dc1 who came at 37 weeks and her birth was a breeze in comparison (dc2 was ELCS due to breech) Try not to worry and good luck.
If you know baby is big intervention is needed I think at this stage. Honestly my baby was almost 9.5 pounds two pounds heavier than first. Midwives ignore me when I told them it's huge. He was measuring large too. I insisted on sweep at 40 weeks and thanks god it worked. But huge baby did number on my stomach and my vagina, I almost wish I had csection. The longer you wait the bigger he gets the harder to birth plus back to back... Unless he turns in labor may complicate thing. Good luck!