Physically hosting your server in a target country does help, but that help is miniscule. In Geotargeting, the largest signals come from your link profile. So if your links come from the US primarily, you should rank better in the US. You also have a genertic TLD instead of a ccTLD, which helps.
Some possible actions to help your site be seen as US would be to do some marketing within the US. Another option is to see if you can get covers.ca and then work on geotargeting that site to Canadians. That would send a strong signal that covers.com is aimed at the US.