I am glad you posted this question. I recently did some plowing and the snow levels and weight were more than six inches. I too charged about $10 more for the plowing on some drives due to the level of snow. Would be curious what others do in this case.
I have found that homeowners do not like to be surprised when they open their plow bills. It leads to a lot of calls and explanations. My take is to price drives so that an average of $200 per hour per truck can be earned for an average storm, and leave the price at that if the storm can be plowed in one pass. If the duration or intensity of the storm warrants, a surcharge of 40% is added for plowing the entire drive the second time. Seems to work.