Final answer:
Smuggling was the illegal activity that helped American colonies improve their status by evading trade restrictions like the Navigation Acts and the Molasses Act, fostering a sense of economic independence.
Step-by-step explanation:
The activity that helped American colonies improve their status, even though it was illegal, was smuggling. Due to various trade restrictions such as the Navigation Acts, Woolens Act, Hat Act, and especially the Molasses Act, colonists found it difficult to engage in profitable trade.
These acts limited the colonies' ability to produce and export goods and imposed high duties which made legal trade less profitable. To circumvent these restrictions, many colonists, particularly merchants, turned to smuggling goods such as molasses, which was a key ingredient in the lucrative rum trade.
Smuggling not only provided the colonies with necessary goods but also fostered a sense of economic independence that would later fuel the revolutionary spirit.