How do Meta geo tags influence the search results?
It is not important. We tend to look at the IP address, country codes, .fr .de There is an option in webmaster tools where you can indicate the relevant countries.
More on geographic targeting
Beware of making changes that try to alter the targeted audience. The example is given of a website that targeted Singapore and then tries to say this is relevant to the USA. The danger is that it may show less in Singapore and not do well in the US.