According to this study, which is quite long and seems fairly rigorous in that unlike other studies it had access to raw data from the retailer, and did not rely on surveys of willing customers, and was funded by the NIH, calorie labelling in fast food restaurants in the southern US resulted in an almost irrelevant increase of 2-6 calories (1%) per item, but a decrease in the number of items purchased of 0.28 items/transaction (5%). However, post-introduction the number of items purchased increased week-on-week
Many other studies are not real world, for example this one with 500+ citations used to justify calorie labelling laws involved recruits who were offered free food. It found a 15% drop in calories.
This metastudy suggests around 7% drop in calories.
Overall the claim that calorie charts cause an overall increase in calorie consumption does not seem to be based in fact; in fact, the opposite. I would add, that while some consumers might choose to consume more calories - for example, if there is a choice between 300 calories of fries for $1.50, or 600 calories for $2, then you might prefer the upsize, it is possible for one group to choose to consume more calories because they are athletic/are sharing food with many people, while others who are obese, might choose to consume less, so the fact that fewer/more calories are consumed, doesn't tell us whether that change is occurring among those who need to consume fewer/more calories.