It it better to do private one-to-one classes on weekdays after school or at the weekend? Are students more focussed after a full day at school or at weekend when they are more relaxed and possibly less tired?
In my experience, this is dependent on the student and sometimes it takes a few tries of trying different lesson times at different times during the week before finding the most suitable time for each student. I find that the older the student gets, the more able they are to focus right after school or after dinner time on school days. The younger the student, the better they are able to focus at weekends. However, I do have a few younger students who do very well after school hours as well.
The most important thing is how much and how often they practice in between lessons and that they practice the aspects that I have asked them to practice. When students feel tired during the lesson and do not seem to focussing as well as they normally would, I makes notes for them on what we cover in the class an ask them to revise all during the week.
To me it seems that, in particular with younger students, it is more important that they are comfortable during the lesson and, most importantly, not hungry. If they haven’t had a chance to eat anything after school, they are unlikely to be able to concentrate well during the lesson. Also, another very important thing is that their phones and other technology devices are not within reach and ideally should be in a different room.
As long as students have had a goo night’s sleep and a at least reasonably good day at school, they are normally okay with doing a lesson after school hours.
Note Corner 
Always go with what seems best for each student!