I have been experiencing this bug since the beginning of 1.6. I like to watch Youtube and play at the same time, as I play Hunger Games and PVP servers a lot. Even when playing single player or with friends I sometimes do.
What I expected to happen was the tab/window to stay the same size, a little more than half the screen.
What actually happened was/is I clicked on a new video, pause the video, etc or even look on the wiki to see how to do something or something like building, but when I click back the window goes back to a "small" size, as if I had just clicked on the Minecraft shortcut.
Steps to Reproduce:
1. Log in. Optional make screen bigger.
2. Make the window any bigger if you haven't already. Don't make full screen though.
3. Open another tab and don't make full screen. If you can, make it half the screen, then do the same for Minecraft.
4. Click on new tab. Then click back on Minecraft.