You can edit each of the module files (ie. includes/modules/shipping/ ...).

Around line 176 in each of the module files you should see something like:
PHP Code:
            $shipping_method = MODULE_SHIPPING_RM1STPACKET_TEXT_WAY . ' : ' . $sw_text . ' ' . MODULE_SHIPPING_RM1STPACKET_TEXT_UNITS; 
'$sw_text' holds the numerical weight, and the constant after it holds the 'kgs'

Remove the last part of that line so it looks like:

PHP Code:
            $shipping_method = MODULE_SHIPPING_RM1STPACKET_TEXT_WAY; 
You may also need to remove the text 'Weight' from the 'MODULE_SHIPPING_name of module_TEXT_WAY' defines in each of the respective language files (ie. in includes/languages/english/modules/shipping/ ...)