I agree that politeness is the best approach. Also, a willingness to pay. On one occasion when I was about 8 or 9 kgs over a standard 20kg limit, the agent raised eybrows and mentioned the weight.
I looked at the scale and said, "Oh yes! How unfortunate - where should I pay." and took out my credit card. They kindly changed their mind.
However, there is a very serious point to all of this and high loadings cost fuel and that costs money and we have to pay. It would be fascinating to know what the airlines budget for in weight and the trade off of those that have hand case only, against those that are fully laden.
I see that SAA is carrying out it's 5 yearly check of pax and their hand cases. THey take volunteers in the departure lounges at JNB for one month and then CPT of one month. They weight pax and hand case separately and then re-calculate their standard loadings.
They sell the information on to other carriers and aviation authorities around the world.