If I could just build on what Jean-René has said, a larger fund gives you better diversification. It also enables you to do what's absolutely critical: you can do the follow-on rounds. Tom can probably address this better than I can.
That first investment a fund makes in a company is not the last investment they'll ever make. It needs to keep some dry powder in its back pocket so that when the company needs another round of financing, it can be there, either alone or with other partners. The larger the fund, the better you're able to do that.