I've almost always been towards the lower end of the healthy BMI range for my height (to the extent BMI is even a meaningful metric), so that wasn't a consideration for me.

That said, absolutely: if you're at all overweight, you specifically need to account for that in your regimen, and train up to running with that load. If you don't, you won't be running for long — one way or another.

I was also never running for pace. I found a comfortable pace and incrementally increased my distance. YMMV.