K.B.
My daughter is over the "weight limit" on her swing and bouncy, etc., but I still use them as she cannot sit up on her own.
As long as you are in the same room to keep a partial eye on him, there is no reason he can't still use the "outgrown" things. The only other thing I would suggest is getting a Hot Sling baby sling to replace the Bjorn. Hot sling is the only sling that comes in actual sizes.