After uploading your image to Blogger or Picasa and adding it inside your post, access the image URL by clicking on the HTML button besides the Compose button.
Change the portion of the image URL as shown below:
http://3.bp.blogspot.com/-O6psiP6KwlE/VCtikOwVTcI/AAAAAAAAMDg/batYPcWt71I/s640/angkorholidayhotel-1.jpgBlogger will then serve the scaled down image for your post with a significant reduction in file size.
It seems that Picasa stores several scaled images of your pics and you can freely adjust the size to match with your blog post. You can try changing to s1800, s1200, or even s320.
If you want to have a square thumbnail just change it to s100-c or s72-c. Again you can choose the size just add the "-c" after for the cropped square image.
For older blogger post, you can still reduce the images using Picasa. Using the Batch Upload function choose the options below:
This will update all the web album folder you choose to the new image size. Not only will this help speed up your blog but it will also reduce the used storage space from your Picasa (800px images will not count into the free storage space).
Please note, I tested this before on a test post and it didn't change the URL for the images after I updated the image size. Kindly test it also before mass updating your old Blogger pics in Picasa.