How did the word "important" come to mean "significant"

I understand the word "import" meaning "to bring or carry in" from the Latin.

I have also read sources which say that the word "important" comes from "importare" meaning "being of consequence"

But how and why did the root word for "bring in" lead to a word meaning significant or being of consequence?

Solution 1:

It seems the stem+prefix import already had the meaning of "care/attention" during the ages of Vulgar Latin. Compare Italian importare and French importer (to be important to, to have matter with). Both of them have totally lost the meaning of "bring in". However Italian importazione has the (original) meaning of "bring in".

There may be a change in Latin that caused the current state of mixed meaning (both "to carry/bring in" and "have significance"). Then it's a Latin question rather than an English question.