Dear Teachers,

1. He's a really sweet guy and seems to have a very good relationship with his family which is one thing that I am very big on.

- "that I am very big on" in this situation means "that I am very impressed", correct?

Thanks very much to Teachers,

to be big on = to be very enthusiastic about; to regard as very important
To be big on something is to be strongly in favor of it.

In your sentence, what exactly is the "one thing"?

There may be two interpretations to your sentence. "which is one thing that I am very big on" could mean that the speaker is very supportive of the idea that a man should have a good relationship with his family.

Or, it could mean that he's big on the fact that this particular man is a good family man.

So I guess you could say being big on something could mean being strongly in favor of the idea, or very impressed with the fact.(I give this fact a lot of weight in judging this man.)

Personally, I lean toward being big on ideas, rather than facts. That is, I lean away from your conclusion.

Best wishes, - A.