Ich traue Fremden nicht über den Weg.

What does “über den Weg” add to the meaning?

“(jemandem) nicht über den Weg trauen” is an expression in German. It means to be suspicious of someone, or to consider them untrustworthy. (source)


Very good explanation of the expression.

However, regrading the original question:

“ich traue Fremden nicht” = “ich traue Fremden nicht über den Weg”
It does not really add anything to the meaning.
It is just somewhat more vivid. Think of meeting a suspicious stranger at a crossing in a dark forest or the like.