To deliberate means to carefully think or talk something through — it also means slow and measured, the pace of this kind of careful decision making. If you chose deliberately, you make a very conscious, well-thought-through choice.
The verb deliberate ends with an "ate" sound — at the end of a trial, after the evidence is presented, the twelve members of a jury retreat to a room to deliberate, i.e., talk through the trial and come to a verdict. The adjective deliberate ends with an "it" sound. If you walk with a deliberate pace, you're slow and steady.