Question

This policy held by the European victors of WW I allowed Hitler to make small gains during the mid-to-late 1930s.

Answer 1

Do you mean WWII? If so, appeasement. Here's more information :) http://history.howstuffworks.com/world-war-ii/historical-introduction-to-world-war-ii4.htm

Answer 2

The Weimar Republic was set up as a semi-democratic government to replace the imperial government. They were forced to sign the treaty of Versailles, which placed all the blame for WWI on Germany. The Weimar Republic went from bad to terrible because of the huge debt owed as restitution for the war and then the world wide depression. Hyperinflation and unemployment fueled extremist groups who had there own paramilitary organizations.
President Hindenburg assumed dictatorial powers to support weak chancellors.The Nazi party gained popularity and control in the early 1930s and made it legal for them to pass laws against the constitution.