Hi you can achieve this using the built in table rates method. Go to system > configuration in admin, then on the left, choose shipping methods and find table rates. Switch the view scope in the top left to your website view (not the store view) to reveal the import/export options. Make sure the condition is set to 'weight vs destination'.
Create a csv like this;
Country Region/State Zip/Postal Code Weight (and above) Shipping Price
* * * 1 5.95
* * * 5.01 7.95
* * * 11 8.16
* * * 12 8.37
* * * 13 8.58
* * * 14 8.79
* * * 15 9
* * * 16 9.21
* * * 17 9.42
* * * 18 9.63
* * * 19 9.84
* * * 20 10.05
* * * 21 10.26
* * * 22 10.47
* * * 23 10.68
* * * 24 10.89
* * * 25 11.1
* * * 26 11.31
etc, upload it, save and jobs a good'n :)