There's no "going into" about it, I made the system, I should know how it works. =P
Let me explain a little more in detail.
Ok first off, the number one affect on file size is the size of your canvas. If you draw large images, you'll take up more space, simple as that.
On 2draw, for each image you have a number of different files. You have the full quality PNG, an optional compressed JPG version (only if it is smaller than the PNG), then 3 different thumbnails (PNG or JPG, whichever is smaller, typically JPG is). Then for each version, you will have 2 small thumbnail versions (which are probably a rather small % of the image total space), and either a JPG or PNG copy of the version (whichever is smaller). Then last of all, you have a format specific to the applet.

As I said above, a PNG version is stored with every image, PNG is lossless compression. Take BMP, one of the simplest image formats around, for each pixel 4 bytes of space are used, so a 400x400 image will use 640KB, uncompressed. Now, PNG will actually compress the information considerably by taking regions of solid color that is, the exact same RGB for a rectangular block of area, and compress it quite well. This means a completely black image at 400x400 can compress to less than 1KB. However, if from one pixel to the next, the color changes (such as with a gradient, soft, or antialiased lines), it can barely compress that at all, and in the absolute worst case (where every single pixel is different across the canvas), your PNG file will approach that 640KB size of the BMP.
JPG on the other hand, is lossy and can compress images better by taking approximations of the image.

For the most part, the PNG and JPG files do not take enough space to cause a problem.

What hits you is the applet-specific format. On PaintBBS, Shi-Painter, and OekakiBBS, an 'animation' file is recorded, which is essentially a recording of each x,y pair of each drawing stroke. This is not really comparable to a video format (which would make huge files). The number of layers, size of strokes, number of undos, etc. all have no effect on the animation file. The amount of time you spend on a picture does not affect the animation size other than by the number of strokes. If you just leave the image open, nothing is recorded. In addition, this is compressed, generally creating a rather small image (less than 100KB) even for extremely elaborate files. So, the number of strokes will in fact affect the animation size, but you need to do a lot of strokes before it becomes significant.

The main difference is on Lascaux Sketch, which uses a bitmap format rather than animation. Lascaux Sketch's LSD format (quite comparable in size and features to Photoshop's PSD) stores the equivalent of a PNG file for each layer into one file. So in this case, the number of strokes, the amount of time, size of brush, etc. does not affect the end file size by any means. However, the size of the canvas, the number of layers, and complexity of the image (read the bit above about how PNG compresses images) all affect the end result.

There are pros and cons to both methods. On average, the bitmap format Lascaux Sketch uses is much larger than an equivalent image stored in animation format. So, from a server standpoint, animation is better. However, the cons of animation format is 1) when you want to resume an image, you have to wait for the computer to "rebuild" the image from the animation so that all the layers are preserved. 2) it is much harder to make a 'stable' animation format. If the animation data gets corrupted or stored incorrectly anywhere in the image, everything after that point will either be completely lost or just turn out plain wrong. In the case of the bitmap format, it is really a matter of what-you-see-is-what-you-get. The layers you had when you saved/submitted your image will turn up exactly as you had when you load it again.

An animation format for Lascaux Sketch has been made, but is currently incomplete (does not support a lot of layer operations, selections, text, and so on), meaning the image would not load back up as you drew it.

dba: just read my comment on the other one... it has everything you need to know.

war is for resources. why? because we waste them.

you know, sucking lollipops is very bad for you. all sorts of bad things can come from sucking a lollipop.

Well, a quick learner you are. I love the starkness of this. Just the almost blank paper... I dunno, something about it is very mysterious. I like it.

You have a very unique, unusual and interesting style to your work. Creative subjects, too.

Beautiful...I love your colors and the water reflections...I'm trying to learn how to do that...pretty pic P.

Beautiful, is it your house pandora?

To me v1 was kind of lonely and desolate looking. This version isn't. It's very nice. I like the subtle shading on the shells. They remind me of those little hand soaps some people have in their bathrooms.

Thanx you guys...hope your Easter day is going well...