There are to main costs for an airline, employee costs and plane lease costs. Employees already are staffed at the check-in Kiosks, so the increase of checking additional baggage should be minimal as in most cases you will not need to add more staff (ERLANG C effect), sure it may add customer wait time, but it is not really an increase in cost born by the airline.
The second cost, plane leases are very expensive, the more miles you can get per revenue dollar, the more the plane pays for itself. If the plane has to wait 15 minutes for people to load their personal belongings, that is non-revenue generating time, no miles are being flown.
I did not say weight didn't matter because it does, it's just not the most important item IMO (industry stands to this to some degree or fashion), and I'm not necessarily against a base fare plus an fee based on weight, but from a logistical stand point, it would be very costly to implement and would hard to recover those costs in the long term.