Er, how does it weaken the economy? The money that the corporations don't get doesn't actually vanish in a puff of smoke, it's still in posession of economic actors, who either purchase something else or invest it in a bank/stock.

What it does is reduce the profit of those corporations, which may make their business unsustainable and lead to this market shrinking, which may cause economic instability while people reorganize their effort towards another market. Those are all hypotheticals though, because the industries affected by piracy are all growing fairly rapidly.

Does competition weaken the economy? There's plenty of examples(e.g. computer hardware) where competition has eroded profit and changed the market dynamics, especially for new entrants. Do clearance sales weaken the economy? Free samples? Does generic medicine hurt the economy? There's so many cases of corporations not realizing the profits they might have wanted, but I don't see how they weaken the economy.