Confess and admit are close in their meaning. To confess is heavier because it's typically used under some form of pressure because you are letting others know something that is not good for you or about you, like in religion (a Catholic confession) or in law (confessing to a murder). To admit doesn't have to be so heavy as you can simply accept the reality of the circumstance (admit defeat) or admit that you're wrong about something, but you can also admit that you murdered someone. To acknowledge is still lighter in meaning as it also means to accept the reality of the situation or you can recognize someone for their presence or their work, either by nodding your head or giving them an award, respectively.