Removing "No Fee" & the weight in the checkout

I would like to remove the weight being displayed in the shipping options at checkout and I would also like to remove "No Fee" from being displayed in the payment options as we don't charge any payment fees.

I have checked the shipping file module pages (/modules/shipping) and can't see where the weight is called.

I have searched the translations and can't see where "No Fee" can be changed.

Can anyone help :)

Thanks a lot.
The weight is output in the option description. You can just set the description to blank. The No fee text is in the view includes/templates/*.catalog/views/ And