WARNING, SPOILERS ARE ABOUND!!!
SERIOUSLY, THINGS WILL BE RUINED FOREVER IF YOU KEEP READING.
OKAY, TOTALLY NOT MY FAULT IF YOU SCREWED UP THE STORY FOR YOURSELF.
YOU KNOW WHAT? I'M JUST GONNA PUT THIS ALL IN SPOILERS JUST TO BE SAFE.
Elizabeth's ability is caused by her extradimensional nature. As you discover, Comstock is infertile so he cannot sire children. Desperate for a heir, he uses the multiverse-spanning machine that the Luteces created to make a deal with a Booker from a different universe. In return for settling some kind of debt, Booker sells his daughter to Comstock, who takes her back to his universe.
Since Elizabeth is not originally from Comstock's universe, her presence destabilizes the fabric of the multiverse. In fact, her extradimensional origin is what gives her the ability to see and open tears.