Aeon does not have a minimum mixin by design. Transactions with mixin 0 can be very small and inexpensive. This is by design. According to smooth If usage increases there is a built in system to limit growth of <2 mixin transactions, thereby preventing the low mixin generated cascading privacy reduction described by the Monero Research Lab as follows:

In AEON the solution that is already implemented is to limit transactions with a mixin (fake outputs) of less than 2 to a maximum of one per block. Since we have four minute blocks that is only 360 per day (though not every block will necessarily have one so the actual number will be lower). As long as there are a few other transactions per block (with higher mix factors), the chain reaction can't occur and everyone's anonymity is protected. You can see for yourself in a chain explorer that when mix 1 or mix 2 transactions occur, they are always in the very first position (after coinbase). Any other transactions in a block will be higher mix.

Currently Aeon usage is insufficient for the cap on very low mixins described above to have its desired impact. As usage increases, the cap will be more noticeable and a fee market will develop: