After being together over 2 yrs, why is he still lurking on his ex's social media? Why is he still so interested in knowing what's going on with her

This does not mean he still has romantic connections to her. Most likely, this ex was likely a big part of his life, as friends and as a girlfriend. It is normal emotions to want to know how an old friend is doing, so I wouldn't jump to conclusions and question him. As he may end up feeling accused. I think the best way to get to the bottom of it, is having an open and honest discussion about you're feelings.