Well the way to build strength is to build muscle. You can build muscle without building mass. Building muscle also increases your metabolism.
Form and concentration are important for weight training, both of which I think would be hard to achieve while walking. You might've built a little strength initially from adding the weights, but 2 lb dumbbells won't take you far. We do have some professional personal trainers and I'm not one of them, but if you aren't reaching failure at 15 reps, then you need to increase your weight. Most women starting out can do well with a small set of dumbbells or an adjustable set of dumbbells.
I would highly highly recommend you looking over the stumptuous.com website:
This a good point of reference for starting out with weights:
http://www.stumptuous.com/cms/displaysection.php?sid=2