Refer to your contract for clarification of all agreed upon times and rates. If you don't have an actual contract signed by both you and your editor, locate any emails, documents and other forms of agreement wherein you came to dollar amounts you agreed to pay. For example, a flat rate of $1,000 was set for a 500-page book expected to be fully edited within two months.
Check the editor's bill against the agreed upon amount. If the editor bills you for an additional amount you did not expect, first call and speak with the editor to ask why there is a discrepancy. Refrain from attacking him and just express your concerns calmly. If, say, the expected amount you were to pay was 50% up front and 50% upon completion, but the final bill is for 70% (an additional 20%), the editor may have a valid reason for asking the additional amount, but you can point out how this was not your arrangement, and you can pay only the remaining 50%.
Tell the editor you plan to pay only the amount agreed upon for the services rendered. If he argues that the costs reflect an unanticipated time overage, point out how that ought to have been brought up before the work continued, when the editor realized the job was bigger than he first anticipated. If the editor insists his rates are valid, ask for a time log or some form of record indicating the actual days and number of hours he worked.
Review the work done. If the bill is for only a small amount over your expected layout, and the work is excellent, mention your dismay at the cost but consider paying it. If the editor has solid rationale for a slight overage, think about whether or not you agree. Go back to the original contract and find anything that states how fees might exceed estimated costs, as in for each hour beyond the estimated 75, an additional $40 will be charged. Make sure you don't embarrass yourself by jumping to conclusions before reviewing the paperwork.
Negotiate a middle-point if you don't want to pay the entire bill but the editor is demanding compensation. Even verbal agreements come with an expectation, so try to determine what you are comfortable with paying and discuss it further.
Contact a person in management or other "higher-up" if the editor works for a publishing house or a team. Simply note the facts, show what you are disputing and why. Perhaps the manager can help resolve the issue more perfunctorily than the editor you were assigned. If you continue to have problems, keep going up the ladder until you get your needs met.