B-12 injections are used a lot of times to give 'credibility' to some questionable doctors who run weight loss clinics. People often feel they are getting something useful because it is injections and extra B-12 won't hurt you, but really the only thing it does is empty your wallet.
B-12 injections would help with 'mood improvement' if you happen to be low in B-12. They do nothing for weight loss. Vitamin B-12 deficiency is easy to test for and usually sublingual drops can keep someone prone to B-12 deficiency with enough B-12. As we age though, our absorption of B-12 by our intestinal tract decreases and the elderly are mostly prone to a lack of B-12. To get their B-12 levels back on track, B-12 injections are often prescribed. For some reason, weight loss 'doctors' decided it was something to use in weight loss clinics. Probably like I said above, because it doesn't really hurt you and people believe it is doing something when it isn't.
You can't out-exercise poor eating habits.