How does lifting weights make you feel physically better?
Yes, it does for a variety of reasons. The endorphin release is not the primary cause though. This is much more pronounced with activities such as running. Beyond the sense of achievement, lifting weights will increase lean muscle mass, produce a thermogenic effect (fat burning), and more generally improve your sense of well-being, as well as strengthening your bones. It can play an important role in preventing/reducing unsightly posture, such as a rounded back and shoulders. These never look good on male or female, with the additional advantage for women that resistance training can help forestall osteoporosis (although good diet is also important in this regard).
Caveat to my first point: It can elevate endorphins substantially as well if you select higher rep ranges (volume) and higher density (short breaks between sets). In fact, done this way the first part of my answer can be ignored. The cardio-vascular load of high volume, low intensity (light weight), high density training will easily exceed most if not all forms of more conventional cardio, with the added advantage of burning fat for up to 2 days, where conventional cardio (treadmill, etc) lasts for a measly 2 hours (in fat burning terms).
So: to distill the essence of my answer: Yes!