There are two explanations.
The first is that when Burns stayed here for a night, he engraved a poem that included cheese on
the window of the house he was staying in (castle house, now the oldest house in the village).
The second is that when the Forth Rail Bridge was being built, the workers who stayed in Kirkliston usually had
cheese in thier sandwiches.
Clearly the latter is the most plausable theory.