Romanias GDP jumped from 122 billion to 214 billion from 2006 to 2008 after joining in 2007.
Poland had a similar jump.
In addition eastern countries receive immense financial subsidies.
Ireland and Luxemburg more or less monetise the fact that they can give companies access to the European market.
For larger countries ( Italy, Germany, France) the benefits are less visible, but being able to negotiate with large markets on eye level is of immense value to exporting economies.
In addition, if you read the Schuman address you might realise that the EU project never was about economics, it was and is about lasting peace. The only founding nation of the union that saw it as purely economic union was the UK.
Finally, anticipating the matter of immigration: Countries like Hungary, Greece and Italy that keep complaining about EU immigration policies, fail to acknowledge that in the absence of the EU they would be left alone with the arriving immigrants from Africa, while the rest of Europe would close its borders.