As people get into more serious relationships, hanging out with friends often takes the form of a double date. While there may be some awkwardness associated with these meals since plus ones may not know each other (or get along), this is generally accepted as part of what being in a serious relationship means. In other words, the seriousness of a relationship can in part be measured by partners' commitment to integrating themselves into each other's lives.
Third-wheeling (or inviting a third-wheel) introduces awkwardness that people often try to avoid by seeing each other without partners or in larger groups so that this social asymmetry is less obvious. I'm curious how much of this dynamic is driven by thoughtful consideration from friends in relationships and how much is driven by single people not wanting to put themselves in these situations.