Come at me bro is a phrase that originated on the reality tv show jersey show. The saying is used to let someone know that you won't start the fight but should it come to blows you won't stop it. You will find jokes and memes that use the phrase with a variety of images. There is even a come at me bro meme of a chic, an actual chic, telling someone to come at them and they will smack the shit out of them.
You will also find pics of things like a frail looking guy telling someone to come at them since they've been in the gym one time. There are also memes with images of skinny justin bieber with minimum biceps definition and flexing captioned with the phrase and showing that he is talking to a man that looks like to be a bodybuilder.