Will they let me be induced for high BMI?

I’m 37 weeks and 3 days now. My BMI is way too high, it started off at 41 at the beginning of my pregnancy and went up to 45 now. I get weekly NSTs to monitor baby. I wanted to ask my doctor if I don’t go into labor by 40 weeks, can I be induced. I know I’m at a higher risk for stillbirth because of my BMI and I know after 40 weeks, the risk of stillbirth increases. Is that something they induce for or should I just not even bother? I don’t want to look stupid!