Personal space is the area around a person that others are not expected to intrude. Invading people's space can be a violation. It can make people feel attacked, mocked, pressured. People become uncomfortable or defensive. Violating personal space aggravates anxiety.
Eye contact is another way in which people can express a range of feelings.
A direct stare can be downright confrontational. Eye contact is often used in a passive aggressive manner, such as refusing to look at someone. Squinting may display judgement, and so on. A quick glance to the side then back will help to relieve the person and show supportiveness. By being aware of gestures and body language you can diffuse a confrontation with a stressed person.