Hi and welcome to DiscussFitess.
If you give more details about your diet, we can help you. For example, post what and when you eat in a typical day. One thing I can see right away is that without eating meats, you need to be extra careful to be sure you are getting enough protein and fats. Fruits and veggies are great (most people don't eat enough of them) but protein and fat are important as well.
As far as weights go, you need to do exercises for all the body parts and not just the arms. You should start off with a full body workout twice a week doing compound exercises like deadlift, squat, rows, bench or dips, military press. If you aren't sure what these are or how to perform check
www.exrx.net and then get back to us with any questions. Another thing is that you need to use a challenging weight. Pick a rep range (for a beginner I'd suggest 10-12 reps) and make sure that the last rep or two is difficult to perform. You have to challenge the muscles in order to see results. Don't worry about getting too big or bulky. If you are female, it simply won't happen because our bodies don't have the necessary hormones to make us big.
Spinning is a great form of cardio, so if you enjoy it, do it. Yoga will increase flexibility but doesn't do much else. The same is true for Pilates.