Constant feeding.... help

ST • In love with my baby boy!
After having my membranes swept, my son was born 38 weeks and 6 days weighing 9 lbs. 9 oz. 22inches... Well since day one he's been eating every two hours. Obviously in the beginning it was about 1 ounce of colostrum every two hours, quickly that turned to two, he is now drinking 3 ounces every two hours at 6 weeks still. Occasionally he will drink some in between, and sometimes he will drink 4 ounces. He is definitely hungry because we check that he's comfortable in every other area. I am so so exhausted, I feel like I do not have a chance to close my eyes by the time I'm done pumping feeding and changing him. At four weeks he was weighing 12 pounds, I assume he is around 13 now? (I pump and supplement due to latching issues)