For the first days I average about 1/2 ounce an hour, I think the fastest I filled the cup was 40 minutes. The Diva Cup has definitely helped me quantify just how heavy my heavy periods are. I've been to several doctors. None had anything to say except that I could go on the pill - which I declined for many reasons.
So it wouldn't hurt to ask a doc, but it is likely they will just say that everyone is different.
That said, the Diva Cup is still the best method for actually containing my periods that I have found. I have much fewer leaks with the Diva cup, but I do have to change much more frequently than women with more typical flows.
With tampons or instead cups and some very heavy cloth pads I generally had to get up at least twice a night for the first 3 days of my period. Last month I had to empty the cup twice the first night (but it was a saturday so I slept like 11 hours) and none the subsequent nights.