Pushups - regular which focus on chest, shoulders, and back; or tricep focused pushups (arms stay close to your rib cage)
Tricep dips (using a stable chair or a couch, or even your stairs)
Tricep kick-backs
rev fly (back)
bent-over rows (back)
upright rows (shoulder)
glute raises (lay on your back and raise your hips - put your weights on your hips for added resistance)
lunges (with or without the hand weights, add an oblique rotation (twisting) or oblique crunch (dipping your shoulder to your hip)
Add balance work -- any standing exercise you do, try standing on only one foot. This adds a good core workout!!
lateral raises (shoulder - raise straight arms out to the side or forward)
add variation to your bicep curl
up for a count of 1, down for a count of 3, and vice versa,
do the "21s" which is seven full curls, seven curls going only 1/2 way up, and 7 curls going from 1/2 way up to all the way up (but not all the way down)
Hold a bicep curl 1/2 up (stationary hold) then rotate your arms out to the side (adds a back/shoulder component)
There are about a gazillion ab exercises using only your body weight!

That's hopefully enough to add variety. Message me if you need more details or more ideas. I've been strength training with a certified personal trainer for 6+ years!