Why did guilds want to influence the city government?

Guilds performed a variety of important functions in the local economy. They established a monopoly of trade in their locality or within a particular branch of industry or commerce; they set and maintained standards for the quality of goods and the integrity of trading practices in that industry; they worked to maintain stable prices for their goods and commodities; and they sought to control town or city governments in order to further the interests of the guild members and achieve their economic objectives.

the population grew a lot and was making more money

increase in population