According to Crispim et al 2011, caloric intake late at night is correlated negatively with sleep quality:
We conclude that food intake during the nocturnal period is correlated with negative effects on the sleep quality of healthy individuals. Indeed, food intake near the sleeping period (dinner and late night snack) was negatively associated with sleep quality variables.
The paper is an interesting read. Here's their figure 1 which shows the correlation between sleep latency (how long it takes to fall asleep) and nocturnal caloric intake:
Thick line: men
Thin line: women
Basically, it shows that people who eat more at night take longer to fall asleep, and other results show that it's also correlated negatively with other sleep quality indicators.