To what extent can the USA and USSR be seen as responsible for increased tensions during the Vietnam War from 1961 to 1972?

Both sides can be seen as responsible, as both sides backed friendly governments in Vietnam. The Soviet Union wished to demonstrate its ability to support an ally. The Communists in North Vietnam were eager to have the military aid of the Soviet Union. During the Vietnam War, the Soviet Union provided much of the weapons used by the North Vietnamese Army as well as the Vietcong. The Soviet Union also sent advisers to the major cities of North Vietnam to help direct air defenses; this meant that American bombers had to be careful in order to avoid killing Soviet military personnel and thus possibly start a larger war.
The United States backed the South Vietnamese government with advisers and money. Most of the people in South Vietnam saw Diem as a puppet, and the United States backed him due to his hard stance against communism. Diem tried to stop traditional Buddhist practices and even insisted on the use of the French language in South Vietnam. When he protested free elections, Diem was assassinated. The United States propped up various South Vietnamese governments even though they were either corrupt or inept. The United States used the domino theory to justify its presence in Vietnam; there was an attitude that the United States had to show force in order to demonstrate to the Soviets that it took defense seriously. The United States also had to look strong to Western Europe by standing against communism wherever it appeared to spread. The United States throughout the Cold War believed that Communist movements worldwide began in the Soviet Union.
In the end, the main ones to suffer in this proxy war were the Vietnamese people. The Americans destroyed entire villages in order to root out the Vietcong. The United States also dropped more bombs on Vietnam than it did on both Europe and Japan in World War II. Agent Orange still leads to birth defects in Vietnam today. The Soviet Union provided little monetary help to Vietnam after the war and the economy was terrible in the postwar years. This proxy war would be a recurring theme in Soviet–American relations during this period, and it would often be the people who lived in the region who would bear the consequences decades later.