Replacing a weight lifting routine with a yoga practice is viable, depending on what you're looking to achieve physically.
Reasons why people weight train:
The "yoga body" that people admire and crave is lean and lithe. Strong muscles are long and supple, not bulky or bulging. The simple fact is that you will have to keep weight lifting if you want big muscles.
However, it is a great cross-training exercise. Adding yoga to a traditional body-building routine is similar to football teams who practice ballet - it keeps the muscles and joints agile and flexible, improves posture and alignment, and can help prevent injury if some muscle groups are developed more than others.
For most weight-loss regimens cardio is the main way to shed pounds, and weights are added in to sculpt and tone the muscles that are left behind.
For people who prefer their muscles to stay lean, and not bulky, yoga and Pilates are both great alternatives. Arm stands, core strengtheners - such as Boat, Plank, or Side-arm Plank - and standing poses are all wonderful ways to build balanced, even muscle tone all over the body - without having to do "reps".
Furthermore, yoga is pain-free, fun and relaxing. Combined with the non-competitive social support of a class atmosphere, it's more likely that students will stick with a yoga practice for the long term.
As we age - particularly women - we must perform a certain amount of weight-bearing exercise each day to maintain or increase bone mass. Weight-lifting has become an essential part of many women's fitness routines as a preventative measure against osteoporosis.
Some women who have already been diagnosed with low bone density are being tasked by their doctors and advisers to do something - anything - that will get them working against gravity. Whether that something is walking, dancing, or yoga depends on the individual.
The important part is being active and doing something you enjoy, so you will stick with it over time. The best part about using yoga as your weight-bearing exercise is that it can be undertaken by anyone - even those who are unable to walk! Chair yoga and Senior yoga classes are commonly offered in senior centers around the country.
Yoga and Pilates will certainly help you increase strength. Some ACE fitness studies refute that it will help you build endurance or stamina, but anecdotal evidence suggests that yoga practitioners are more physically fit and better prepared for endurance trials than other athletes.
Perhaps it has to do with a deeper awareness of one's body and the sensations? Perhaps it is the strength and flexibility of supple muscles that are ready to do what you ask? It seems that more investigation in this area is needed.