We offer discounts for non saturday nights
Why? Simple. it works. People that have events on friday or sunday are usually doing it to save money, so they are looking for a deal.
More importantly, we usually have tons of availability for a Sunday. We have had 10 weddings booked on a single Saturday and maybe 1 or 2 Sundays all month, so I always have guys willing to do them. It's extra money to them and me.
If I could book sundays as easily as saturdays, I wouldn't offer a discount.
Yes, my costs are the same and we don't make as much on a sunday gig as a Saturday gig. But we make much more on a booked, discounted Sunday gig than we make on a regular priced Sunday gig that we didn't book.
Everyone has their own opinions on whether to discount or not, but if the reason you can't discount is because your regular prices are already as low as you can go, it might suggest rethinking your pricing structure so you at least have some wiggle room if the situation calls for it.