I don’t think it will count against you. I think it is something you should write about in your essays to add depth and understanding to who you are. The amount of time and psychological toll that it takes to care for a parent is very significant and it may be to your benefit to explain how this had an impact on you. You are human and only have so many hours in a day. I don’t think they can expect you to have significant other activities since this is in essence a full time job.