My T used to frequently let me have an extra session if I was feeling bad (as in not quite suicidal but seriously distressed). Then a while ago he started offering only phone calls. A couple of weeks ago we talked about this and he stated that he did this on purpose. When I told him that I thought that was unfair and mean, he agreed and we agreed to change it back to that if I feel I need it, we can meet, given he has a free slot.

It's not exactly the same as your situation since your T never offered contact on weekends in the first place. But it's still asking for a change in some boundary things. I think it's reasonable to ask for it. But you also have to be prepared for the fact that your T might not want to respond on weekends. If you are open to that or maybe some compromise (for example maybe Friday or Thursday evening, or some other way of making you feel connected like a transitional object or similar), I think it's perfectly reasonable to at least ask.

I don't think you're asking too much, but I can also see why your T might not want to offer contact during his free time. It's always okay to ask though. If nothing else, at least it helps your T understand what you need and maybe there's a different way that you can get the thing you need.