Market makers covers a broad range of shops, from large investment banks to small proprietary trading firms. So working capital can be in the millions or the billions, and leverage can be anywhere from 2x to 30x. This is no different from buy-side firms, which includes a variety of both asset managers and retail investors. There is tons of diversity among market makers.
As for contribution to volume, a liquidity provider merely quotes a price; the trade doesn't happen until a buy-side counter-party decides to accept. For example, given a trade of 100 shares between a market maker and an asset manager, we wouldn't say that the market maker was responsible for 50 shares of the trade. We would just say that 100 shares were traded.
With this in mind, we can claim that the market maker is responsible for all trading volume, or we can claim that the market maker is responsible for no trading volume (and that the buy-side firm is responsible for all volume). Either seems plausible.