Answering the narrow version, because the broad one does not have a single answer. HbA1c reflects roughly three months of average glycaemia weighted toward the most recent weeks, which is why repeating it at six weeks tells you very little. The improvement on this class comes from two directions — direct glucose-dependent insulin secretion and glucagon suppression, plus the indirect effect of weight loss on insulin sensitivity — and the second continues after the first has plateaued.
Happy to go further on any of that.