Just delete the lines of code referring to shipping and tax. They won't calculate or show until after the checkout confirm page is visited, but if you continue to shop they will appear on the cart page, so just delete them where you don't want them.
Probably the shipping is set to base on the weight field instead of the totalweight field in the shopping cart. It could also be using the value of a single row instead of the ColumnTotal for that column. You would have to look at where the weight was specified to see which of those two it is.