My arms look like that and when I was doing weight training consistently they did not get bigger. They got smaller. So, it really just depends.

My arms are very similar to yours. It's too soon to say if they'll get smaller for me as I'm only 11lbs down, but as I was gaining, my arms were always disproportionately larger than the rest of me. Still hoping it'll go away, though!

Please don't use light weights with lots of reps! It is a waste of your time, and one of the oldest and hardest to kill myths in women's fitness. You need to lift heavy weights to get results. Women do NOT have the hormone balance to get bulky without a TON of effort and time (think eating calories above your maintenance level and gaining only about 1/2-1 lb. of muscle per month). However, lifting weights just builds the muscle underneath the fat--you have to diet to lose the fat before you can see the results of your hard work.