I do believe you. But only in theory.

In one of my previous places of employment, there was a very short guy. He was nerdy, lived with his parents even though he was 46 or 47, and had never been married. Very smart but not rounded (meaning - smart professionally and enjoyed math a lot, but had not read fiction), very together (perceptive, financially independent, hardworking, and nice), but - never married. So, there might have been issues.

there was also a very tall guy who rode his motorcycle to the office. He was tall and muscular and had a lot of "presence" in the room when he would walk in holding his huge helmet. He had a wife and a couple of children and was basically a successful male with a lot going for him.

When the shortest guy wanted to talk to the tallest guy and tried to get his attention, it did look awkward. Indeed.

But that was an extreme case - the shortest guy was very short, and the biker very tall.

You do not qualify to complain about being discriminated based on height - your height is sufficient for you to not feel the way you report feeling. Your case is not extreme. In other words, yes, it exists, but it should not affect you personally.

In terms of reality checking - there have been studies showing that tall guys enjoy premium wages. Look them up. So it does exist.