There is extensive evidence for the benefit of the Mediterranean style low carb diet, including cutting your risk of heart disease and diabetes. It has even been found to reduce risk the risk of breast cancer, compared with those on a low-fat diet. Consuming extra virgin olive oil (the fresh squeezed juice of olives) seems to be particularly beneficial when it comes to cancer, perhaps because it contains compounds such as polyphenols which are known to be anti-inflammatory.
I too have been a yo-yo dieter for decades and I ended up paying WW to actually put ON weight. Then I discovered LCHF and well … the rest is history as they say. The main difference between Atkins and LCHF is Atkins never really focussed on whole foods (just think of their range of shakes, bars, candy etc) they are also reported to eat much higher protein and most of their phases aren’t actually keto, more of a low-carb “ish” plan and may include some sugars and grains. Why not join the FREE support group (no money required) and learn all the tips and tricks and my stepwise method to get you back on track. Welcome aboard!
Use fat as a lever.  We’ve been taught to fear fat, but don’t! Both keto and low carb are high fat diets. Fat is our source of energy as well as satiety. The key to understand, though, is that fat is a lever on a low carb or keto diet. Carbs and protein stay constant, and fat is the one you increase or decrease (push the lever up or down) to gain or lose weight, respectively. So if your goal is weight loss, eat enough fat to be satisfied, but there’s no need to “get your fats in” once you’re satisfied.