It´s a great question and it often come up in my class. There are really two fundamental reasons we use weights.
The first is that in traditional yoga, we often use muscles that support the front of the body (e.g. our pectoralis, our core, our quadriceps) while the back of the body often times, gets neglected. To complicate things, we often live our lives front facing too (in the sagittal plane). What that means in layman terms is that our bodies tend to move forward (e.g. when we are walking, driving, on the computer or even brushing our teeth). As a result, our bodies and thus our skeletons tend to tilt forward. After a while, if we don´t strengthen the muscles in our upper back (the rhomboids, the trapezius, the latissimus dorsi), those that are responsible for pulling our bodies or skeletons back, our bodies begin to slouch and round, thus creating poor posture and making us more susceptible to injury. So where do the weights come in? When we use weights in yoga, we incorporate exercises that specifically target the upper back muscles and squeeze our shoulder blades together and down the back effectively pulling us back and creating a nice balance in the body.
The second reason is to strengthen our bones. We tend to forget that our bones are alive and if we put healthy stress on them, they grow. For example, when we are in Warrior 2 and performing bicep curls, the muscle that sits on the bone is actually forcing the bone to get stronger to support the additional weight. As a result, the bones get stronger and are less susceptible to injury or osteoporosis (fragile bones that are more susceptible to fractures). As we age, this becomes even more important as we tend to lose bone density. Luckily, adding weights to your yoga, counters this effect and enables your bones to stay strong and healthy. Thus, why wouldn´t you want to add weights to your workout?