How do airlines without assigned seating verify cargo balance?
The cabin crew simply counts the seated passengers (or alternatively empty seats) by zone (a block of rows), writes it down and hands the slip to the flight crew. It is common to do this on commuter planes even with assigned seating since passenger balance matters more on small aircraft and people may move.

As pointed out by SKYbrary:


  In practice, low cost airlines, which routinely offer free seating, also operate the majority of their flights with a high load factor, so that identifying any unoccupied seats will be a fairly simple matter.