My old mattress had this problem. It was some major brand name and it just eventually sagged in the middle. My wife hated it, so when we moved into our new house, we ditched it and went to Macy's, which has a remarkably large mattress selection. (Plus, if you time it right, they will sometimes have significant sales.)

We ended up dropping something like $4K on a king size Macy's-brand mattress that claims it need not be flipped or rotated. It's "firm", which we both prefer, yet has a layer of memory foam on top so it's not like you're sleeping on a board. Four years in, we're still completely happy with it. My wife, in particular, used to complain of lower back pain with the old mattress and she loves the new one.

For size comparison, I'm 5'11" and 195 pounds, so in the same ballpark as you in terms of the damage I do to a mattress.