The justification for that microprice is empirical, not theoretical. In most market I can think of, most of the time, if there are more orders and more size on the bid than the ask, then it's more likely that that BBO will tick up rather than down. And the greater the imbalance, the higher the probability of an uptick (and vice-versa for downticks). For ...
Here are some classical papers:
Cont, Stoikov, Talreja: A stochastic model for order book dynamics, 2010
Cont, Larrard (2013) Price dynamics in a Markovian limit order book market, SIAM Journal for Financial Mathematics, Vol 4, No 1, 1-25, 2013.
@amdopt's answer emphasises there is a lot of depth to this topic and that the actual behaviour of the order matching depends on exchange particulars. In this answer, I give a simplified view of an exchange where market orders also don't match other market orders.
Orders can be split into two types: resting orders and immediate orders. All resting orders ...
Two (or more) orders arriving at the same time makes no difference for an exchange's matching engine, the buy orders execute against sell limit orders, and the sell orders execute against buy limit orders. If no limit orders exist, market orders may be rejected by the exchange, or the price will be restricted to a 'volatility threshold' based on the last ...
Market orders cannot be matched against other market orders. Consider this case:
1) Limit book is empty on both sides
2) Market sell arrives at same time as market buy with matching sizes
What price do you fill this trade at?