I have been doing some form of Strength Training serially (on for many months, then off for a while). Originally it was to build strength for performance in sports, then just for recreation (I enjoy how my body feels when I am lifting consistently).
It has been generally accepted that to build strength and size, you need to lift heavy. McMaster University, in my hometown in Canada, released a report a few months ago on research that seems to indicate otherwise. Link is posted below, but the quick synopsis is that it seems the most important aspect of the lifting = strength/size equation is taking the muscle to failure - in other words, until you can't lift that weight anymore.
It doesn't seem to matter whether you lift heavy or light, just go to failure and you will gain.
So if you have working out with weights and are wondering why you aren't gaining strength/size, it could be you haven't been going all the way to failure on each set.
Unless you are working with a trainer or spotter, going to complete failure has challenges. Most people lose form (proper from/technique is critical in injury prevention) as the muscle weakens and are then more susceptible to injury. If you want to go to complete failure, I would suggest working with a trainer or seasoned spotter to assist in maintaining form.
I mostly workout at home and haven't yet trained the hound to be a good spotter (oh, she's critical of my technique all right, but can't lift enough weight to be helpful).
The approach I have developed over the years is a modification of drop-sets (progressively lighter weights) and only going to technical failure (to the point where I can no longer lift that weight with good form/technique).
You can even do drops within a set. For biceps curls you may start at 30 pounds for 8 reps (technical failure), then 20 pounds until TF, then 10, and finally 5 - at this point you may not even be able to lift your arm, but you have achieved complete failure, while mitigating the risk of injury.
Have fun lifting - here's the link to the article: