It's not a question of how much exercise you can possibly tolerate but exactly what is the correct dose of exercise that is required to make improvements in strength and muscle mass. Women who slowly and modestly gain more muscle will change their body composition. Such women will have more lean body mass and less fat. If you're one of these women, you'll look a lot better. Now here's another key point, and it's closely related to the fear of getting too big.
Muscle weighs more than fat.
Training will strengthen and reshape a woman's body, and she may weigh slightly more than before she started training. However, the scale weight is not nearly as significant as a woman's body composition. Women who are effectively training should not simply depend on the scale. If you need to have your progress quantified, aside from the increase in strength you'll be showing, consider having body fat measurements done every month or so. That's where you'll notice some meaningful difference.