Would it help airlines, if they knew passenger weight before hand?
Despite of the "delay" during the check in procedures, it would be safer than the average companies usually use. 
For instance, the latest FAA guidelines on aircraft weight and balance control set individual passenger weight averages at 190-195 pounds for adults and 82 pounds for kids, depending on whether it's summer or winter. (Based on the assumption people wear heavier clothing in winter.) 
I have read an article, and there are more pieces of information.

Airline begins weighing passengers for 'safety'