chiefly British : affectedly or excessively dainty, delicate, cute, or quaint
In other words: sickeningly sweet.
Some things I might describe as TWEE: any rom-coms featuring Meg Ryan, roses and baby's breath, fourteen-year-olds engaging in PDAs, people talking to babies or (forbid) tickling their feet, perhaps anything described as "SO CUTE!!!!," beanie babies (do these even still exist?), home decorations that involve sailboats, seashells, or anything in the style of "Cape Cod," and many types of reunions.
Some things I might describe as literally sickeningly sweet: mountain dew—especially the new varieties in various shades of red or purple, caramel, buttercream frosting, toffee, butterscotch, and any "coffee" drink that comes from a machine you would find in a 7-11.
I'm going to stop here before I begin to feel ill.