To answer the specific question, I believe the largest hf in the world is Bridgewater (assets under management of around 120bn USD). Assets of around 500m USD would be considered average and north of 1bn usd large. Bridgewater is an outlier. I do not know if one larger has ever existed but I doubt it.
As to what effects they have on the economy well, funds can serve as catalysts for economic events (e.g. Soros' fund and others catalysing the UK exit from the ERM). They serve as vehicles for pooling and allocating capital and so act as intermediaries between those who wish to lend (investors in the hedge fund) and those who wish to borrow (firms issuing bonds etc. which the hf buys). This function only applies when the hedge fund is making a primary investment though - when it is buying something in the secondary market rather than a first issuance funds do not have this role. They largely determine things like commodity prices, exchange rates through the bulk of money they control together, although no hedge fund is large enough to control these markets directly.
