Courier companies all have different hours that they work, but standard operating hours are going to likely be near 6AM to 6PM. Anything outside of these hours is going to count as an afterhours delivery. Although courier companies have a great many fees and surcharges which may be tacked on to any shipment, overweight shipments being another prime example, there aren't many fees which will cost you as much as afterhours shipping, however, if this is essential to your business, then you may be required to pay for those fees despite the cost. The same sorts of fees can also apply to holiday shipping. A Chicago courier service will usually apply an after hour surcharge in one of two ways. Some companies will choose to assess a flat rate for any delivery that is made outside of their normal business hours, whereas other companies will opt to charge a percentage of your total bill instead.
The best thing to do is simply to spend some time researching the company you are considering using for after hours deliveries. Most companies will have their fees listed clearly on their website, so some time spent doing research with Google should help you to learn which companies can save you some money in this regard. In Chicago as an example, there are far too many companies for the scope of this article to compare all of their afterhours fees and surcharges, however, if you spend the time researching them you may find some deals that can really make a difference in your companies shipping costs.
The most important thing is to realize that this is completely dependent on the amount that you foresee your company needing to shift during this time period. If you think that you're going to need to ship after hours on a regular basis, then taking the time to find a company which specializes in 24 hour delivery with no surcharges or fees could save your company astronomical amounts of money. On the other hand, if your company has scheduled deliveries only once a week during the morning, then this isn't even something you need to worry about. You may find a company that charges outrageous after hours fees, but they may have very affordable scheduled service which will actually be a larger asset to your company. As always, it is more about finding something that meets your company's needs than about finding the lowest price on services that you don't even require.