Although I could go on for ages about the intricacies of Venetian Society, I'll limit myself to answering your very poignant and focused questions. Feel free to ask-follow ups.

By the twelfth century, the Venetian Republic was facing several internal and external pressures. Indeed, this was a time period when most Italian Cities were affirming their new independence by rallying around urban Bishops. However, Venice had always been independent and had no need to rally around their Bishop, who happened to hold the very important temporal title of Patriarch of Grado (whose existence was contested by the Patriarch of Aquileia anyway) and was more a nuisance than anything. In fact, the Venetians not only insisted on taking an independent line between the Church and the Italian cities in their fight against the Holy Roman Empire, but even actively ignored the conflict; preferring to focus energies to help the Byzantine Empire fight a war against the King of Sicily and reaffirming Venetian rule in rebellious trade outposts in Dalmatia.

Managing relations with an increasingly active and politicized clergy, a state of war just over the lagoon on the Italian mainland, Venice's own war in Sicily, and the pacification of the Istrian cities, could no longer be performed solely by the Doge and his inner circle of friends and advisors. So his inner council was replaced the 35-man Concilium, which would function as the Doge's ministers and council. All members were acclaimed for life by the Arengo, the mob-like assembly of all inhabitants of Venice.

By 1207, population growth meant assembling the Venetian mob every time a Councilor dropped dead went from being impractical to being almost impossible. So instead of nominating each member of the Concilium, the Arengo nominated three "Electors" whose job it was to pick men to serve in the Concilium. However, this system was also less than ideal, and by 1230 the mob started acclaiming however many wise men they thought were sufficient to pick a suitable council, sometimes picking as many as seven electors.

The the government of Venice had also been growing: the Concilium had been increased to 100 members in 1172, effectively constituting a state bureaucracy. In 1178, the Doge was no longer elected by the Arengo, but by the Quarantia, an assembly of forty men. These forty were nominated by the seven-or-so electors acclaimed by the Arengo.

So Venice was becoming gradually more undemocratic. Why? In part because of governability, but also because "Proclamation by Mob" isn't always the best way to pick members of government. The Arengo favored strong, popular candidates, who sometimes had undesirable hidden qualities. And its unsurprising how the Doge who ruled before the Quarantia was Vitale Michiel, a member of the old landholding nobility from the vicinity of Chioggia. Michiel was no-nonsense, energetic, and tough; however these policies translated to bad diplomacy and warmongering.

Michiel was unable to stop the Pope from placing the Bishop of Zara under the purview of the Patriarch of Grado, which the citizens of Zara used as a pretext for a revolt against the Republic. Only an unpopular military expedition, where many citizens outright ignored calls to arms, brought the city back under Venetian control. Michiel also sided with the Pope and the Lombard Cities in their wars against the Emperor Frederick Barbarossa, resulting in a crippling land blockade that was only broken after a costly naval attack down the River Po. Pisan and Genoese privateers, with Imperial backing, would continue to stifle Venetian trade. Lastly, a disagreement with the Byzantine Empire led Michiel to organize an absolutely enormous military expedition, but Emperor Manuel Komnenos cleverly set up circuitous peace talks as the Venetian army and navy were worn down by attrition in the Agean Sea. When the disease-ridden and exhausted army came back to Venice, they were so livid that Doge Vitale Michiel was lynched.

With the Republic's own army running amok and the city plunged into anarchy for nearly six months, the electors decided to take matters into their own hands and proclaimed the elderly merchant Sebastiano Ziani as Doge. Although there might have been some misgivings, the Venetians were primarily concerned with getting back to normality, and Ziani's rule was enormously succesful. Ziani worked to broker peace between the Lombard Cities and the Emperor, making Italy safe for trade again (Ziani had also shrewdly got the northeastern Italian cities to turn on the Emperor, and join forces with the cities of Lombardy). Public works were undertaken, including a large project refurbishing St. Mark's square. When Sebastiano Ziani retired to a monastery at age seventy-eight, although electors evidently didn't feel like they could immediately proclaim a Doge, they chose forty wise and upstanding citizens to constitute the Quarantia, who picked the well-respected judge Orio Mastropiero. If someone had any complaints, none were recorded.

By the time the 1286 proposal was made to make membership of the Concilium hereditary, the majority of actual work running of the country was done by the Minor Consiglio or minor council, a small collection of advisers nominated by the Concilium. The Concilium itself became known as the Maggior Consiglio, or Major Council. This Council, which by now can be said to resemble a legislature, was still selected by electors proclaimed by the city assembly, however this was not only seen as a major nuisance, it was pointless: members of the same important families continued to be elected anyway.

However, the first proposal to "seal" the council proposal was shot down. A similar proposal in 1286 was put to a vote by the Arengo, but was unsuccessful (unsurprisingly). Finally, a significantly watered down proposal was passed in 1296. The Major Council would nominate members of the Quarantia, who became the supreme court, governors of the mint, and were charged with evaluating new individuals to be admitted to the Major Council. All members who had participated in the Major Council in the past for years were automatically admitted. Each year, forty new members, chosen by the Quarantia from the descendants of the existing members, were admitted to the council, bloating its size. In 1315, the so-called "Golden Book" was published, a stage registry of all persons who held the right to sit on the Great Council, and a new law was passed allowing current members to register their male children after their twenty-fifth birthday.

What did the ordinary people think of the change? All the evidence points to the fact that they were rather indifferent; the only major revolts came from people registered on the Golden Book (famously, Bajamonte Tiepolo in 1310) and it might have very well been a relief for the city's inhabitants to not have to assemble every time there was a need to select a new. The gradual reduction of democratic rights by the ruling class as well as the appearances of inclusive institutions made the changes easy to stomach ("This is your Doge, if it pleases you!" were the words spoken by the head of the Quarantia to the assembled crowd after each election).

In the short term, each change made the Republic easier to govern. However, make no mistake that even after reducing enfranchisement, the Republic was absolutely obsessed with inclusion; by the fifteenth century, little over 2700 individuals had the right to sit in the Great Council! This obviously made for an unwieldily decision-making process.

It is also important to note that the Venetians also had a different conception of nobility than the rest of Europe. Someone like Vitale Michiel, for example, who held lands south of Chioggia was most probably very similar to what you would expect a nobleman to be. Although he lived near the Parish of San Giuliano in the city of Venice, his militaristic policies and blunt decision making style paint a picture resembling a traditional European noble, plus his wealth derived from owning land; clearly at odds with the rich but cautious and diplomatic merchants whose families would be listed in the "Golden Book." Make no mistake, the Serrata was a seizure of power by an elite, many of which possessed wealth handed down through generations, but there clearly was something about the Venetian elite that made them seem accessible and identifiable to the ordinary citizens of Venice.

The above is all covered in the authoritative text on Venetian History: John Julius Norwich's History of Venice. It's a must-read for anyone interested learning about in the City and Republic of Venice.