Ho-kay... I have no idea what version of paint you're using, but I busted out mine from Win XP Home and my graphic editing software and did some poking around. I do some more or less self taught graphic design and try to solve problems by futzing with things till they make sense, heh...
When I opened the Atributes window from the Image drop down at the top of the screen in Paint, it gave me the option to resize, using either inches, cm, or pixels. At the top of the window, it gave my test picture's size in bytes - in my case 37,724 bytes. That is equivilent to 37.724 kilobytes (kb).
There are many ways to change the file size to a picture (you may find an "Optimize" option in some software) that include resizing, changing the resolution, or changing the file type (like from a jpeg to a gif or vise versa).
The easiest way to do what you're trying would be to change the measurement from pixels to inches or cm and reduce it by those more familiar measurement types. Or you can try just punching numbers in for pixels and experiment
If, like in my Paint software, your paint is showing you file size in bytes, then you need to get your bytes down to 256,000 bytes or less (equaling 256 kb). Just try reducing the picture's printing size (by inches, cm, or pixels) and see what it does to the file size (in bytes or kb). Just be careful when you save your newly resized picture that you don't save over your large picture! Alter the new saved name a little so you can tell them appart (I'll often call something pic.jpeg and sm_pic.jpeg to keep them appart).
File type can make a huge difference in size, but that get's really complicated to explain why - suffice to say the difference between, say, a jpeg and a gif file is how the file tells the computer to "make" and display the picture, and more importantly, the colors. If you have software where it's easy to change file type, I'd try just switching the type from one to the other without resizing print size and see which one makes it smaller, then work from there... Usually you have to "Save as" a new file type or "Export" as a new file type.
Also, if you have a resolution option, that can make a big difference too. In Fireworks, my graphics software, the option is called "quality" of jpeg, gif, etc, and I have a slider and percentage window to toggle the resolution up or down. Of course, the lower the resolution, the smaller the file, and the more distorted the picture may apear.
If this was totally incomprehensible, I'm happy to try to explain it better either here or in private message... Otherwise, I hope this gives you some things to try!