Lifting weights won't make you too bulky!
This is a huge misconception and anyone who does lift will tell you they wish it was that easy. Find the fittest person at your gym and ask them how long it took them to look like that. I'm betting the answer won't be "a couple weeks." So, why does this misconception exist?
I think most people know that they aren't going to touch a barbell and wake up tomorrow with a set of rippling biceps, yet it's a concern I hear all the time. Many times the real barrier isn't actually a fear becoming too muscular, that's just the reason that's given. A lot of times a fear of trying something outside your comfort zone leads to this aversion to weight training. I don't mean to belittle this feeling. It can be very intimidating to start something new, especially walking into a gym and trying to learn how to lift weights, but being scared is rarely a good reason to avoid something.
Another reason I hear is a worry about getting hurt. This is a concern I can actually get behind. In fact, I don't recommend that beginners try to teach themselves. Go work with a trainer, even if it's just a couple sessions. A little guidance can go a long way to helping you get the most out of your workouts and avoid poor technique that can lead to injuries.
Everyone should incorporate free weights (barbells, dumbbells, and kettlebells) into their workouts. This doesn't mean that the weight needs to be extremely heavy or that it has to be in every workout, but it should be progressive and varied. That means 3 sets of 10 with those 3 lb weights isn't going to cut it for long. Remember when you learned how to drive and 35 mph felt like 100 mph? Now you don't even bat an eyelash as you set your cruise control at 75 mph. The more we do something, the more we adapt and that same stimulus becomes less challenging. Doing the same exercises, at the same weight, and the same repetitions will have diminishing returns the longer you do it. We can apply this to body weight exercises too. Walking, running, and other body weight exercises are important, but their potential to build muscle is limited. That requires loading.
The big picture is developing and maintaining lean muscle mass for longevity and better quality of life. Muscle mass is one of the most accurate factors in determining health later in life, not blood pressure or BMI, but lean muscle mass. Nothing builds muscle more effectively than weight training. The question isn't why should you lift weights, but how much and how often. Again, this is where I would recommend talking with a trainer (or your favorite weightlifting chiropractor!) to learn where to start and how to progress your workouts. Happy lifting!