Nuggets : At London photo studio, the precursor to “say cheese” was actually “say prunes,” to help sitters form a small mouth. A more presentable shape for better photoshoot results.
After doing some research on the web, I have summarized everything into the following few reasons.
1) Firstly, "Cheese" contains the phoneme /i/, a long vowel which makes our lips stretch to make a smile. I'm not very sure why "cheese" was chosen instead of other words to be the universal smiley word.
2)When we say "Cheese", we mouth tend to form a smile or an impression of a smile,
the corners of your mouth turn up, your cheeks lift and your teeth show.
3)By saying "cheese" we also bare our teeth which is the desired photo pose.
4)It is said that "cheesing" is a slang term for smiling. We also found out that the Persian word "chiz" means "thing," hence the expression, "This is the real chiz (cheese)."
Nuggets 2 : Picture-perfect smiles weren’t always the norm, says Kotchemidova. The photos of the nineteenth century were ruled by stony, solemn faces. These early photos took their cues from traditional European fine art portraiture, where smiles were only worn by peasants, children and drunks. The etiquette and beauty standards of the time also called for a small, tightly controlled mouth.