Empathy is a great strength for me, as well as weakness. I find high value in being empathic, as I can bulid better relationships, ask more questions to understand where another is coming from or taking a moment to think about how might feel about an experience.
Having empathy in designing software makes me think of Kathy Sierra's Making Badass Developers that was required watching for the for the Capstone. Remembering we are humans, not humanoids. Taking that into consideration and actions will speak for itself. Emapthy also asks to us to take the user into consideration into development. It can help us develop a more intuitive site that has a more effective, perhaps, profitable, useage & result.
To truly be empathic is to be an active listener - and I am trying to ask myself "Why am I talking?" when asking a question. Having that in mind when working with a team is key to being productive. It allows trust to build so when someone offers you feedback, or you are offering them feedback, such input can be taken positively.
I have found that when you have truly taken a moment to know your co-workers, empathy is natural. I've used it when my co-workers have had medicial emergencies, or sudden deaths in thier families. So much so, I've been called on my personal phone when one was sobbing. The best empathy to have is to listen, and know that your words don't mean a lot, but you listening does. There is great strength in being that person for others.
When I find empathy hardest to use is when I am being judgemental, or shame myself when another has a better question or understanding around a topic. When I find myself in those moments, it's very easy to not have empathy towards others, and have a more hateful attitude. I have those moments, and I name it, and try to remember that I'm human, and others are too.