Some antidepressant medications can cause weight gain, especially the older tricyclic antidepressants (TCAs) such as Tryptizol, Saroten, and Clomipramine; as well as newer drugs such as Remeron (Mirtazapine). Lithium (for manic-depressive disorder) often causes weight gain. The most common antidepressants known as SSRI’s (for example Citalopram and Sertraline) usually don’t impact weight significantly. More on depression
The first meta-analysis worth noting collected the data from 10 randomized trials comprising 1376 participants in total.  After analyzing the research, a key relationship emerged between dietary carbs and blood sugar levels. In short, the researchers described their finding thus: “the greater the carbohydrate restriction, the greater glucose lowering…” 
On a ketogenic diet, your entire body switches its fuel supply to run mostly on fat, burning fat 24-7. When insulin levels become very low, fat burning can increase dramatically. It becomes easier to access your fat stores to burn them off. This is great if you’re trying to lose weight, but there are also other less obvious benefits, such as less hunger and a steady supply of energy. This may help keep you alert and focused.