I've run into this type of problem before, when supporting a school. At a particular time of day, the Administration Wi-Fi would go crazy for a limited amount of time I checked and rechecked, and then went back to basics -- researching Wi-Fi radio interference.
Can you guess what's high on the list? ... The human body!
Sure enough, the Administration Wi-Fi was affected by the sudden influx of families each day ... when the people left, the Wi-Fi went back to working as expected. A bit of further investigation yielded that the Wi-Fi access point was not ceiling mounted but placed on a bookshelf (about 4.5' high. So moving the access point to the ceiling solved that problem immediately!
Often when people ask for Tech help regarding their home Wi-Fi, I advise placing their Wi-Fi (router and access points) as high as possible, given a home environment and furniture. With just one or a couple of persons resident this isn't a strong requirement, but with a larger family - i.e., multiple bodies moving around -- it becomes more important.
Give it a try.
All that said, it also could be that when usage is up on the weekend, the traffic is simply greater than your Wi-Fi system can handle. This isn't always just about bandwidth capacity, but the number of device clients and the traffic activity are definitely factors.
