Final answer:
The British government did not allow more American settlers to move past the Appalachian Mountains to avoid conflicts with Native American tribes, maintain control over the colonists, and collect taxes more easily. They feared that settlers in remote areas would become independent-minded.
Step-by-step explanation:
The British government did not allow more American settlers to move past the Appalachian Mountains for several reasons. First, they wanted to avoid antagonizing the Native American tribes in the Ohio Valley and prevent costly new wars. Second, they wanted to maintain control over the colonists and enforce their imperial laws more easily. Allowing settlers to move beyond the Appalachians would put an increasing number of colonists out of Parliament's reach and make it more difficult to collect taxes. Finally, the British feared that once the colonists were remote from the control of royal officials, they would become increasingly independent-minded.