Question

What are reasons a strong nation would want to extend their political economic and military control over week or territory

Answer 1

Another way your question could be framed is “why do nations use imperialism on weaker countries?” and the simple answer is there are several motives such as ethnocentric purposes, religion, access to natural resources, expanding power, etc. Specifically people resort to imperialism on weaker countries because they are vulnerable to accept whatever helps the people survive in times of unrest.