(1) The tick size puts a lower bound on the bid-ask spread (and often is equal to the bid-ask spread)
Tick size too big: the bid-ask spread (which the market maker earns but the customers pay) is too big. Favors the market-makers at the expense of the customers.
Tick size too small: vice versa.
Therefore the tick size influences the transaction cost.
(2) The tick size is inversely proportional to the number of levels where limit orders can accumulate.
Tick size to small: many price levels to choose from, relatively few limit orders at each price level (short queues). Relatively little depth at each level and therefore frequent small changes in price (microvolatility).
Tick size too large: few price levels, each with many limit orders queued. Prices stay constant for a long time without changing, but limt orders take a long time to move to the front of the queue and get executed.
Influences the "cost of immediacy" i.e. whether limit orders or maket orders are favored.