This is an exceptionally interesting question! In short, this is a rather complicated one because instead of having 1 solid overall-answer, you really have 13 different answers that also varied by time period. I don't have the ability to write 13 different answers, so I'll try and answer this by first talking about a beacon of democracy, but then using an example of how restricted democracy could be in other states. So let's jump into it!

Some colonial governments that were established by 1700 were much more democratic than the institutions that came before them, however this varied on a state-by-state basis. Some states, like Pennsylvania had been established in the late 17th century to be specifically more democratic than colonies or countries elsewhere. In Pennsylvania, it was created as a haven for Quakers who were fleeing persecution in England and was, as such, enabled to have a legislature that not only allowed many men to run for office, but allowed the majority of men to vote for those positions. The Pennsylvania Assembly held great power but also was at the whim of the people behind it. This set the groundwork for when Pennsylvania set up their own constitution in 1776, they created arguably the most democratic state constitution of the entire period. However, this was not the case everywhere, where some states struggled to have democratic power in their government.

The Case of Maryland

Maryland was settled by English colonists in March 1634. Initially, it was initially settled to be a Catholic haven, specifically for Catholic Englishmen to flee during these turbulent times in England. Here, the government started to show signs of a budding democracy almost immediately even though it, legally did not have to. The colony was under the rule of Lord Baltimore who legally owned all the land that comprised 17th century Maryland. However, a colonial Assembly was created in 1638, which forced the government to begin acknowledging the rights and laws granted to them in England. The colonial Assembly held significant power for the next few decades, even during periods of religious violence in the 1650s. While the Assembly was limited in terms of scope and power compared to modern democracies, they still held power where many people in the colony could have a say. The following year, in 1639, Colonists were worried that their own assembly could resemble the House of Commons in England which hadn't been summoned in over a decade. To fix this, they made it mandatory that their own assembly meet at least once every three years.

Soon thereafter, The Assembly split into two bodies, between the Lower House and the Upper house-- the upper house having more power and consisting almost entirely of the richest men in the state (the Lower House was still comprised of wealthy white men, but the requirements for property and paid taxes were much reduced for running for office as compared to the Upper House). The upper house also had a governor -- all appointed by Lord Baltimore. This caused tension though, since from the 1650s onward the two houses feuded enormously due to conflicting interests. It's also worth noting that the colonial governor, who was appointed by Lord Baltimore, had some control over the Lower House and could hinder some of their own measures while they were in session.

Maryland underwent significant changes to the structor of their government following the "Glorious Revolution" in England. The government switched from being a proprietary colonial government to a "royal colony", which placed it's leadership directly under the British Crown without a colonial Lord anymore. The King of England could now appoint his own governor to enact his will (this same thing happened almost everywhere across the colonies). The power of the colonial governors was significant, however the one democratic victory the Lower House gained the right to convene without the permission of a colonial governor or leader. This was a major step in Maryland's history towards an embrace of democratic ideals since it allowed colonists to appoint their own leaders and meet on their own without permission from the crown.

Maryland's government acted with certain democratic ideals through the 18th century. For instance, in 1718, the Lower house published a single volume that listed every law that had been passed in the colony since the new government had been started. They also continued to be a voice of 'the people' through the 18th century since all appointments were made by 'the people'. However, this doesn't tell the full story. Maryland's 18th century legislature was extremely undemocratically created. Property requirements to even run in the lower house were very stringent, effectively banning 92% of all white-males from even running.[1] Property requirements to even vote were also heavy, with about half of free-white males being allowed to vote. Also, unlike other colonies like Pennsylvania, Marylanders who were eligible to vote could only vote on their Lower House representative. Local positions, even local sheriffs were appointed and Marylanders had no say over who held those jobs. Maryland made some changes to this once the Revolution started.

During the 18th century, Maryland's legislature had some power, but it was always done under the conditions of knowing that they were subservient to the British crown and Parliament. They could pass laws, but their scope was limited since anything that was passed by them could be overturned or strike down by England.

It's important to note that no state legislature had the power to contradict the legal will of the King or British Parliament. This was the foundational issue that set the stage for the American Revolution, since in the 1760s, colonists found themselves being taxed and having unfair (in their view) laws passed against them (like the enforcement of mercantilism) where they had no democratic voice to speak out against it.

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I hope this helps. It's a complex topic but I hope using Maryland as an example helped provide insight into this period.

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1] Ron Hoffman, A Spirit of Dissent, pp 179 - 183

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Which colonial society? French? Dutch? Belgian?