Prolonged eye contact can be a measured sign of confidence, and most people will not hold that with another person for more than a few seconds at times unless they really know them well. In other circumstances (not yours), prolonged eye contact can be considered awkward and off-putting - I really believe it depends on how well the two people in question know one another, as to whether they're comfortable with the prolonged, direct eye contact.
It's intimidating, because it shows courage. Most people, I'm generalizing in American society, tend to be kind of shifty when eye contact is underway. I also noticed greeting each other affectionately here as opposed to an Eastern country also causes some discomfort, like a kiss on the cheek. not all the time, but certainly under some circumstances.
You aren't weird, if that's what you're wondering. I think it shows you are confident and honest, because sometimes it is hard to have direct eye contact.