Big transactions have more impact on the price. After a fork people look at price as the primary signal of which fork is dominant.
Discussion
Why do big transactions have more impact? Do you mean big as in payload size? Like batch transactions, consolidations and coin joins?
Because big in sats doesn't affect the bottom line for miners, maybe for users who are eyeballing the network, but not for the rest of us, and not if the fork has a rule change with it.