Hehe.
Ok, so right now 3lb *might* be your limit, but I promise you if you lift weights regularly (like 3x a week) you will VERY quickly outgrow 5lbs. Also doing aerobics holding weights is VERY different from actually lifting weights. One adds additional tension to your muscles while you're doing a cardio vascular exercise. It's a different use of the muscle and it doesn't provide the same result as actual lifting.
How will I know when I've done as much as I can do with the weights I have?
From everything I've read and what I practice in my own lifting, is that you'll see the best results using somewhere between 60%-80% of your 1 rep max. What that means is that you test yourself to see the heaviest you can lift one time. And remember that each exercise is different - you should never pick one weight and use it for every exercise. For example, I can squat 100lbs, but I can only bench 65lbs.
So start there. Pick an exercise .. say a bench press. Then start adding on weight to see how far you get before you can't do the exercise any more. Obviously, the more you do, the tireder you'll get, so try to estimate as best you can as quickly as you can. So if you can barely lift the empty olympic bar (which weighs 45 lbs), then you could figure your best most effective weight to be, say, 30 lbs (65% of the bar). An EZ bar (the one that has the curved hand grips) usually weighs around 25 lbs. So you could add 2 2.5lb weights to the EZ bar to start out with.
After that, if it gets so that you can do 3 sets of 10-12 w/out struggling to complete the 3rd set, you're not getting any benefit any more. It's time to add weights.
Now, those are the guidelines I use based on research. They're not the only right guidelines. Some people say to start with less weight. Some people say to start with more. Some people say 3 sets of 12, some people say 5 sets of 5. There are benefits to each and every method depending on what you're trying to achieve.
But I think for someone just starting out it's easier to say .. here's my starting weight, and now I just add more when I'm not pushing myself to lift these anymore. Make sense?
Are pushups as effective as lifting weights? Plank? Do I even need weights at all if I can do regular exercises using my own body weight?
Body resistance exercises are VERY effective ... there are a ton of things that you can do and not have to have weights. I know a lot of people who have made impressive changes to their bodies doing nothing more than bodyweight work.