Final answer:
US support for Batista was due to his anti-Communist stance which aligned with US foreign policy, giving the US economic and strategic advantages in Cuba, especially with regard to the sugarcane industry.
Step-by-step explanation:
The support of Fulgencio Batista by the United States was primarily because he opposed popular Communist movements in Cuba. US foreign policy in the Caribbean has long been driven by preventing rival nations from gaining control over regions close to the US mainland, with Cuba's proximity being a significant factor.
The US tolerated Batista's undemocratic rule because he held a tough stance against Communism. During Batista's dictatorship, the US had control and cheap access to Cuba's sugarcane industry, making it a matter of economic and strategic importance. Although Batista's regime was brutal and his repressive actions shocking, the US continued support under the notion that the dictatorship prevented possible left-wing uprisings.