"Seeing is believing"
>Whatever you see by yourself, you believe that it exist, despite the fact it is unusual or unexpected.
The phrase "Seeing is believing" implies Skepticism. It means we will not accept the truth of something unless we can somehow see it. It ask for supported conclusion or verification. We are tends to not believe if we haven't seen through our own eyes. We will not accept the fact that it is true unless we see by our own eyes. But we believe the fact even it is unusual or unexpected if we see by our own eyes. So this phrase implies that you don't believe those things which you heard people saying but believe the fact which you see through your own eyes.
In our modern society where most of the people are educated it is hard to believe in such thing which we haven't seen. Whatever we see it has supported proof to it. We don't believe in others unless we see by our own eyes. But in our society there are still many things people believe eventhough they haven't seen one yet. For an example, everyone in this universe believe in God which they haven't seen yet but still believe it exist. Here for this example we can use the phrase "Not-seeing is believing". In other words, we do not believe what we see; rather, we believe what we do not see. It is where faith play great role rather than seeing.
For the above phrase we can use Abraham as the perfect example of faith.Without knowing exactly what he would find as he followed the inspiration of God, Abraham left his home of origin and journeyed through a foreign land. Abraham did not see, yet he believed. He clung to God’s promise of descendants, even though to him it seemed an impossibility. He did not see, yet he believed. The greatest test of his faith came when he was asked to sacrifice the very child who was to fulfill this promise of descendants.
Faith is the realization of what is hoped for and evidence of things not seen.
I think what quote "One eye-witness weighs more than ten hearsay" tries to mention is "those who hear, say what they hear and those who see knows clearly". It means people will say whatever they heard to other people eventhough they didn't know either it is true or not. Eventhough they haven't eye-witnesses it they tell other people but those who have seen knows clearly either it is true or not. Having a eye-witness on something that is unusual but exist weighs more than people saying it doesn't .
So people believe in what they see. But there are still things that people believe eventhough they haven't seen one yet, where faith plays greater role than seeing and believing. People believe in those thing because it has lot of history supported with proof which people knows from the time they born. And sometimes it is better to believe in those things which you have eye-witness on it rather hearing from people.