Hi Meghan,
I can easily hand hold the Sigma 50-500 or 120-300 + 2x (the second combo is twice as heavy). I've even used the 600/4 handheld, but my wife can't do the 50-500 handheld, and she's not weak.
However, most of the time, we both use a monopod (Manfrotto 682 - largest and strongest they had at the time, you'll need it), since that added stability helps alot. Especially since you're not always shooting in full-sun - nor do you want to either.
There's also a fair number of different xx-400mm zooms available, many for under $1000-. Ebay has a few for around $500-600.