Don't know about weekends (I had no idea that there were weekend dates?). As for AM vs PM, you are randomly assigned. This is from the ECFMG's scheduling page:
When you confirm a testing appointment, you will be assigned to either an AM or PM session. A PM session is assigned if, for that test date and center, AM sessions have been filled and PM sessions have been opened.
(The same way that you are assigned a random available center in cities that have more than 1 examination center like Philadelphia.)
I think that centers that offer PM sessions have also scheduled them already, but I can't say for sure.