What can I do to keep a Sheppard Hook from leaning over?

I add a stick or a rock to the hole to brace on both sides of stake sometime I wedge a broken rock underneath the long ground part to brace...a rock generally will have a side with a bit of a dip in it///I place that "dip area "right under the long portion that is connected to the stake that goes down in the ground...also if you do your bracing after a good rain when ground is soft ...the ground will dry hard around your brace and give it more stability.

If it's on a decline, dig down and put a stone under the soil. at the level you want it to lean . you may have to repeat this a few times taking into consideration that the pot gets heavier when you water it, and the stone may settle in.

Ok. Use cement ,but put it in an empty coffee can and bury it. This way you have stability and it can still be moved.

I put in one of those metal fence post sunk in the ground and them put in the sheperd hook with the post in the grove in the post. If need be put a zip tie or two for further stability to stay in the groove in case of higher winds that will move the hook. It works really well. I have a couple that I did that were on a slight hill. All you have to do to move the hook is cut the zip ties and pull out the hook and put it in the next area. I too use a shepherd hook type bird feeding station for two feeders and two suet blocks.

depends upon where it is, if there is something to attach them to, wire or other materials work well

Lay heavy concrete blocks around it to stabiize it.