Have One's Way Meaning

Example : 1898, J. Meade Falkner, Moonfleet, chapter 5:  He held out to me a bowl of steaming broth, that filled the room with a savour sweeter, ten thousand times, to me than every rose and lily of the world; yet would not let me drink it at a gulp, but made me sip it with a spoon like any baby. Thus while I drank, he told me where I was, namely, in an attic at the Why Not?, but would not say more then, bidding me get to sleep again, and I should know all afterwards. And so it was ten days or more before youth and health had their way, and I was strong again; and all that time Elzevir Block sat by my bed, and nursed me tenderly as a woman. So piece by piece I learned the story of how they found me.