When we weight train, we are slowly increasing our metabolism. We are actually burning more calories at rest. So our bodies end up burning more calories throughout the day.
The other thing to keep in mind is this. Most of the time when people want to lose weight, they want to look good. They want to have a physical appearance they're proud of. While running or walking is going to burn fat and make you look slimmer, it's not going to give you that lean physique that most people are actually aspiring to get. That's achieved by weight training and by building up bigger and stronger muscles.
Now, many people say that one or two gym workouts a week is sufficient to do this. But if you really want to lose fat and make a change, I would recommend getting in at least 3 workouts a week. The big thing with getting in at least 3 workouts every week is this. It's the identity shift in the way you look at yourself. Yes, building muscle once a week is a good thing. I know many people who do this. They have a gym membership (for which they are paying a lot of money), and to justify the expense they force themselves to go to the gym once a week (or twice at the most). The big thing with training at least 3 times a week is that there are 3 different recurring moments every week when you tell yourself something like, "Yes, I am an athlete. I'm the type of person who gets himself to the gym and trains and looks after himself." This attitude helps reinforce and rebuild the way you look at yourself -- not as an occasional "gym goer," but as an athlete who is fully committed to taking care of the temple God has given him. And that just helps the way you look at yourself. You also have the added bonus of (1) burning more calories because obviously you're training more and (2) the benefit of building more muscle and becoming a leaner version of yourself.
Just a suggestion!