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Larger transactions have higher execution costs. Larger funds have larger transactions. It probably isn't the case that there is a linear correlation between fund -> transaction -> execution cost but it is a close enough approximation that everyone is mostly happy.

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Additionally, at least with Vanguard, if you have a lot of money invested you get access to funds with lower costs. For example, for $3,000-$10,000 you can VFINX which costs 0.17%, but if you have more than $10,00 invested you can buy VFIAX, which costs 0.05%. For $5M and up, you can buy VINIXm which costs 0.04%.

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