George Weber’s classification first appeared in the article “Top Languages: The World’s 10 Most Influential Languages” in Language Today (Vol. 2, Dec 1997).
Weber’s taking into account and giving points (in parentheses) according to six factors: number of first language speakers, number of second language speakers, number and population size of countries where the language is used, number of major fields using the language internationally, economic power of countries using the languages, and socio-literary prestige.
The world's top ten most influential languages:
Even though based on now outdated information Weber writes in 2006 that the ranking remains unaffected.
An interesting classification of languages according to a composite index based on the number of speakers and the number of countries where a language is spoken:
Louis-Jean Calvet Le marché aux langues (2002)