Are the deadlifts and squats helping to reduce weight and burn fat?
Unfortunately, double-blind case studies are few and far between in fitness, so most people simply regurgitate what they have been told or base their opinions on anecdotal evidence. Today, I will do the latter... It's all I, or most others here have.
My personal experience is that a pure anaerobic workout of heavy lifts resulted in massively increased cardio capacity and overall fitness. It was very few weeks before I noticed I didn't need to breath hard going up hills, etc.
After a very successful year of that, I had dropped 50 pounds, which I estimate to be a loss of maybe 70 pounds of fat combined with a gain of about 20 pounds of muscle. Something in that ballpark anyway. At some point in there I was 40 years old, dead-lifting 420 with a body weight of 170. Also doing 7 minute planks by the way.
But, and here is the funny part... I could still "pinch an inch". I really wanted 6-pack abs, and I didn't have them. So instead of continuing what was clearly wildly successful for me, I started running and swimming. Everybody says aerobics are better for weight loss, so I shifted to them.
I tend to obsess on things, so after a year or so on this path, I was running multiple 10Ks per week. I logged 130 or so miles each month for a couple of months at the peak of it. And... I weighed about 180 after those two years... 10 pounds up, which I estimate to be in the ballpark of a loss of 10 pounds of muscle and a gain of 20 pounds of fat.
I don't begrudge people their cardio. But the idea that cardio is the best way to lose weight seems to be based on faulty science. Unhealthy or overweight people who start cardio tend to lose weight. For various reasons, most people who want to lose weight and get healthy start with aerobic exercises like running, spinning, etc. And when they lose weight, they rightfully credit their aerobic workouts.
All of these people lose weight because activity beats inactivity. And doing aerobics will increase fitness and help shed pounds for anyone who is unfit or overweight. The missing piece in this analysis is any valid comparison to anaerobic workouts... You cannot compare aerobic activity to inactivity, and conclude anything about the relative benefit of anaerobic activity.
We come to the question: "What will work for you?" There is little good science to answer that question, so you will have to do it yourself. 6 months should be enough to give you a real sense of it... Take a before picture, and make some notes about how you feel going up a hill or playing a sport for an hour or something. Then work hard on your lifts for 6-months and take the after picture. And compare how you feel doing various activities. Decide how to go forward based on your results.