Many times, we get to know our subordinates, and as they are usually good people, we let things become too easy, too friendly, and we lose our ability to be the supervisor. If you give a good person an opportunity, most will take it, even if it is your job they are taking.
There is a fine line between being a cordial, respectful boss and being so agreeable that your assistant inappropriately decides that you are equals. It can be difficult to bring the relationship back to where it should be, once you have given too much ground.
You may have to discuss the situation in a direct manner and reclaim your authority by writing out duties and obligations. Of course, you must be prepared to follow through, and it can cause stress in the short term, but if you have chosen your assistant wisely, they will appreciate your leadership ability and abide by your decisions.
Remember that this person was chosen to help you and that your qualities and experience bring something to the workplace that your business needs from you, not from other workers. Your assistant must respect boundaries, and you are the one that has to create and nurture those boundaries on a day-to-day basis to keep things running smoothly.