I can’t really think of any document construction strategies that would affect file size, other than
1. paying attention to the image settings in the Publish Online Options dialog
2. Limiting the number of fonts used in the document, keeping in mind that bold, italic, etc. are all separate fonts, and each font ends up embedded in the document
As far as I know, InDesign’s Object Export Options for individual images are ignored by Publish Online, so that doesn’t help.
Keep in mind that for certain animated effects and transparent effects, InDesign will rasterize regions of the page in order to reproduce these accurately, and this may affect file size in unexpected ways.
I do think that for testing purposes, using the FXL HTML Export script that David linked above would be a good way to compare file sizes for Publish Online output. But bear in mind that the script doesn’t include any control over image dpi and quality settings. But it would be a good way to test to see if changing something on the page makes the resulting html larger or smaller.