Weekend pricing, especially during the summer months, will affect you, no matter which moving option you may choose. Truck rental companies like U-Haul and Penske will have higher prices per mile, along with greatly decreased availability on the weekends. The least affected moving companies will be those that supply moving containers, like PODS or U-Pack. Since their rental periods are often a month or longer, renting these on a weekend instead of a weekday shouldn’t be much more difficult.