I have a hairline crack on the balcony concrete slab which is only visible from the bottom. When it rains the water leaks through this crack. I want to know what I can use to repair the crack once I remove the tiles and will the crack get bigger or reappear?

Where do you live? I would recommend having this evaluated by a structural engineer. A crack big enough to allow water to seep through could indicate the slab is not safe for a balconey, you would not get me on it.