I've heard that if you eat sweets after big foods, your stomach gets the energy needed to digest and probably bigger part of your lunch will get digested (so it won't transform to fat).
Are there any reliable studies on this topic?
It might speed up digestion:
But speeding up digestion isn't going to bring you the outcome you desire. Also, a larger amount of simple sugars is more likely to lead to increased energy stored in adipose tissue (fat cells).
Big foods - those with larger, more complex molecules with stronger molecular bonds - such as more complex carbohydrates, proteins, and fats, take longer to digest, and a combination of these and fibre further slow the overall process, meaning that the energy being released into blood-sugar will be less likely to become surplus to requirements and lead to those larger spikes in blood-sugar levels which trigger storage.
There are things you can do to stimulate or assist the digestive system, like chewing well to start the process, ingesting bitter foods and drinks to stimulate bile, a shot of vinegar if you have low stomach acidity, or even the sort of enzymes you find in things like lactose free milk which contains lactase (although this turns a disaccharides into two more quickly absorbed monosacharides so it's only really recommended for those who are lactose intolerant). A high fibre diet will also improve your intestinal flora long term, as well as it's short term effects on digestion.
Technically an unhealthy and under-active digestive system would be more likely lead to less fat, as the body loses some of the ability to absorb macro and/or micro nutrients, meaning they pass through the system.
In a depleted state, such as after prolonged starvation, or in a diabetic crash, a quick sugar hit might be needed to kick-start the system, but in general the body can easily find the energy it needs, especially for a process as slow and steady as the average 24 hours it takes to digest a meal.
There are things which can reduce cholesterol re-absorption, such as increased fibre, medication, or supplements (although I've heard plant sterols as a supplement can be Sisyphean). Excess cholesterol isn't really about energy though.