"influence increased" is a correct and usable phrase in written English.
You can use it to describe how something has grown in strength or power, for example: "The organization's influence increased as more people joined their cause."
As Gupta influence increased, sculpture gained in importance.
He'd long pushed for a larger role in Westboro, and after the elders came to power his influence increased.
After the death of Maria Theresa's husband, the Holy Roman emperor Francis I, Kaunitz' influence increased.
Their influence increased in the 1880's as they founded and ran factories like the Rookwood Pottery Company of Cincinnati, which employed mostly female artists.
That influence increased with fame, and it will be apparent in the international cast of dancers descending on the Duke Theater this week for the New York City Tap Festival -- especially since Mr. Glover will take the stage himself.
Russian influence increased after the collapse of the Ch'ing dynasty in 1912 and particularly after the consolidation of the Soviet regime in West Turkistan.
However, the influence increases with the increase in the size of the company.
Choosing j determines how dependent seed assignment is on the CTB information, where CTB influence increases with j.
A comparison between forced convection and free convection results illustrates that airflow influence increases in airflow windows.
A common characterization of adolescence is that parent influence decreases and friend influence increases as adolescents age.
In so far as Henry had a policy it was to generally push back on papal influence, increasing his own local authority.
