While it is not true that all Austrians welcomed the Anschluss, many did. The main reason for this was that many Austrians were happy to be part of Germany. Let us look at two reasons why this was so.
First, Germans and Austrians were essentially ethnically identical. Up until the 1870s, there had been no separate country of Germany. The area that later became Germany was broken up into many little independent states. Austria was, in those days, seen as one of the most powerful German states. Therefore, Austrians did not feel that they were that much different from the Germans and were happy to be united with them.
Second, since the end of World War I, Austria had been weakened. As a result of that war, Austria lost its empire and was reduced to being a second-rate power in Europe at best. Soon after the war, many Austrians started to push for a reunification with Germany. Austrians wanted to get back to being part of a major power and Germany looked like it was becoming such a power under Hitler.
For these reasons, many Austrians welcomed the Anschluss.