Weight is a measure for the quality of the move.
NOTE: This is sometimes referred to as count.
The Polyglot book generator sets it to 2*(wins)+(draws), globally scaled to fit into 16 bits.
WARNING: Older Polyglot versions are defective as to the use of zero weights, (meaning the move should never be played), and crash when they encounter them.
This because of a misplaced internal consistency check, which really only made sense during book building (which deletes all entries with zero weight from the book).
Yet hand-tuning of a book often leads to the desire to completely disable a move, without deleting it.
Some software approximates an entry with zero weight by giving it very low probability.