Myth busted... lifting weights as a woman DOES NOT make you "bulk" up. In fact the benefits of lifting weights are great; I can't recommend it enough when starting a fitness regime. I understand the fear for a beginner walking into a gym and wondering where on earth to start, but that's what a personal trainer can help you with and I'm sure that any instructor within a gym would be happy to give some guidance too.
I've come across a few people in my time as a trainer who are scared to start lifting for the fear of bulking too much. To respond simply, women do not have enough testosterone in order to build muscle in the same way a man does. Don't get me wrong, women do still have some testosterone in their bodies - some a little more than others - but we will not build muscles as big as a man would, especially for a female who is lifting only once or twice a week. Chances are that for a beginner you will also not be able to lift anything too heavy in your first few weeks or even months of training since you need to build up the endurance to lift before you have the strength and power to lift.
Muscular endurance and strength training will help to "tone" and condition the muscles over time, building lean muscle which in turn helps to metabolise fat. This gives the muscles a more aesthetic look that most people are aiming for - we don't want to simply lose weight and excess skin if we have the opportunity to lose weight and build the muscle at the same time. It's also important to note that men on average have lower body fat percentages than women to start with, so to get those "washboard abs" that some of us have been waiting for takes a little longer to achieve on some occasions, and can also come down to a healthy balanced diet.
It should be taken into consideration that women starting to go through, or have been through, the menopause start to suffer from osteoporosis, or the loss of bone density from the change in hormones over time. This means that it can be easier to break a bone at an older age, and it'll also take longer to repair itself. By doing weight-bearing exercises, even with low weights, we can slow down the process of osteoporosis alongside a good diet, and therefore lower our risk of serious injury at an older age.