Final answer:
Colonial legislators were elected by property-owning men, with assemblies exerting significant power in legislation and budget control. They represented local interests, differing from the British practice of virtual representation, with efforts made for equal representation in states like Pennsylvania and North Carolina.
Step-by-step explanation:
Legislators in colonial assemblies in North America were typically chosen through an electoral process overseen by local county or township administrators. These colonial lawmakers were often selected from among the property-owning class, based on the wider distribution of land ownership which allowed more men to meet the property qualifications to vote compared to England.
Assemblies like the House of Burgesses exercised significant political power, including the initiation of legislation, controlling the budget, and providing a forum for free speech and the immunity of its members during sessions. The right to petition the monarchy for redress of grievances was also a crucial function of these assemblies.
Over time, these assemblies expanded their influence and were composed of men who were seen as having a direct duty to represent the interests of their local constituents, differing from the British concept of 'virtual representation.' Furthermore, some states like Pennsylvania and North Carolina made efforts to ensure equal representation through constitutions that set provisions for representation based on a number of taxable residents or set numbers of representatives from each county.