I flew IAD-CPH a few weeks ago and the check-in agent weighed my carry-on roller bag and was insistent that it couldn't weight more than 8kg. I almost panicked before I reminded her I was flying business and suddenly there wasn't a weight limit any longer... This was a slim roller bag, not anything that looked stuffed.

I wasn't able to avoid the check-in desk as I needed to show my passport there to get my boarding pass. If you can get your boarding pass on mobile I would go that route.