Thank you so much for identifying this weed, and for the advice! I didn't know it would take over so quickly! I am going to remove it, although reading through the all the vitamins/minerals his plant contains (Omega-3, Vitamin-A, B, C, minerals, iron, etc.) I feel like I should make Purslane soup for dinner!
I am not sure I am brave enough to try to taste it though, but it is good to know that something like this weed could be so beneficial for our health!