I came to notice I was naturally an empath a couple years ago when I started journaling about my day consistently. I notice some trends that seemed to go unnoticed until I took an objective view of it later. I had started spending time around some people more often than usual and noticed I seemed to take on the emotional state of the person I was with. For example a old friend of mine (more fool than friend) used to spend time around me a lot. He was typically always in a angry, the-worlds-out-to-get-him state. Within a few seconds of hanging around him I'd adapt to that mindset too. Then I could go around someone who was completely happy, having a terrific day and mimic that myself. Not only that, but I could easily tell when others were playing a facade while they were hurting, or mad, etc, etc. I still do all this today and I have to say it's so incredibly annoying.
What's strange about me is that around people, I adapt in how I speak to them depending on how they feel, who they are, etc. It is kind of like, I will talk to one of my instructors one way, but another differently and perhaps a bit more informal, and then someone else differently, etc.
The same thing also happens to me sometimes, but I don't normally allow it to happen.