I fuse my pieces with Wonder Under (not stiff at all) and use Presencia size 8 Perle cotton. Be sure to let the fusible cool completely before you attempt to tear the paper off. I've been known to pop the pieces into the 'fridge for a few minutes...
Betty, LOVE your piece! I'm wondering if you may have used Heat & Bond? It's not meant for applique, but for crafty things that don't get sewed down. Horrible stuff...almost impossible to hand needle and makes your project feel like cardboard.