T2D patients also have a reduced amount of insuline-producing beta cells. At diagnosis, there's been a 50% destruction of insuline-producing beta-cells. The destruction progresses with the disease.
In my case, my liver seems to emit a virtually endless amount of glucose, This is probably why I'm fat, and oddly, when my diabetes is well controlled, I'm never hungry, when its poorly controlled I'm hungry all the time and gain weight - which is how I was most of my life, being hungry virtually 24/7, even when my blood sugar was normal.