Syrupy things are very, very sweet—probably a little too sweet! A syrupy dessert might make your teeth hurt.
Things that are literally syrupy have the drippy, sticky sweetness of molasses or honey. If something is figuratively syrupy, it's so sentimental that it makes you cringe, like syrupy love songs or syrupy greeting cards. The adjective syrupy comes from syrup, "thick, sweet liquid," from the Arabic sharab, "beverage."