How to prevent my bike from tipping over when using just one pannier? I often carry gear in a pannier on my bike rack, as in the photo below (not my bike, but same pannier design. My actual bike frame is very different; I'll upload my own picture tomrrow):



I have two panniers, but typically only use one because I usually have to carry the bag around with me at my destination, and carrying more than one bag becomes cumbersome. 

The problem I run into is that when fully loaded (not beyond capacity, but close to it), my bike tips over when I prop it up with the kickstand. I always put the pannier on the same side as my kickstand, as I've learned that it tips over easier when on the opposite side.



What can I do to prevent my bike from tipping over when the pannier is too full? The easiest solution would be to distribute the load between two panniers, but that's impractical because of the challenges with lugging around two bags once I'm at my destination. 

Do there exist kickstands with some sort of platform on the bottom to help stabilize them? Is my kickstand not positioned/attached correctly? Or is there some better way to balance things out so that my bike won't tip over?
You have a few options here. 

You can get a two-legged kickstand. These are primarily used with heavy touring loads, but they will help stabilize the bike when parking with an uneven load. The two legs fold up into each other when you disengage the kickstand. You generally cut these with a hacksaw to shorten them to the appropriate length. I used one for a while: 



However, that may be overkill. You might look into what's sometimes called a brake-band by the maker of the Click-Stand, an add-on for a parking stand for touring bikes. (The stand itself - a kind of tent-pole-like thing with a rest on the end that the bike leans into - would likely be overkill for am everyday use like this.) 

This'll hold the brakes on while the bike is parked, and stop the bike from rolling while parked. (You can purchase them from the click-stand site, or just make your own with pieces of velcro.) Here they are, hanging on the side of my bike in between uses:



Finally, if you're not too picky about your paint job, you can simply decide to go without a kickstand and just lean your bike against a wall or a pole, or lay it on the ground.