If you have a broken metabolism, with stubborn residual insulin resistance (liver, not adipocytes), or your leptin receptors are screwed up by WGA from wheat and your satiety switch is broken, or any of a number of theoretical metabolic derangements from years of eating the standard american diet, you may have trouble losing weight without going VLC (say 5-10% carbs) and you might indeed gain weight if you eat excess protein beyond your needs.
The extra insulin response to excess dietary protein may simply drive more fat storage. I would not expect this in most people, but it may happen in some.
What to do?
If you can't lose weight and you need to, you must cut carbs until you have ketones in your urine. Ketones in your blood is ketosis. Ketones in your urine is ketonuria. Ketonuria is proof of ketosis. GNG (gluconeogenesis) and ketosis is the sure way to prove your insulin levels are low as you can get them.
Then, as dietary fat has the least effect on serum insulin, and dietary protein has a small but measurable effect, eat only the minimum necessary protein (.8 -1 g/Kg/d) and the rest as fat.
5% carbs should guarantee GNG and ketonuria. (This will mean almost no vegetables and no sugary salad dressings, etc. Your food must be naked except for healthy fats)
15 -10% protein (drop it as you adapt)
This, by the way, is ridiculously easy to achieve if you use butter and cream, but a bit impractical otherwise.