There are a few factors that contribute to this. The main ones, I think, are a fundamental view of society and economic ties to Britain.

A Hierarchical View of Society

The social structure of the English-speaking world of the 18th century was predicated on deference. Every person had a their place in society, and was expected to both respect their social betters and maintain their superiority towards their social inferiors. Wealth and success could allow a person to move between ranks (indeed, this was one of the things that theoretically defined American society), but could not do away with the underlying structure. This degree of flexibility and mobility is what allowed the same people who wrote and fought for the belief that "all men are created equal" to believe that people with less money than them should do such thing like avoid direct eye contact and bow deeply as a show of respect before all social interactions. Slavery, of course, was harder to square up, which is why the Founding generation was generally willing to consider it a necessary evil.

It would be incorrect to say that all loyalists loved this stratified, inherently unequal organization of society. Some were poor, and many were runaway slaves. However, the leading loyalists were wealthy, established landowners and merchants who very much enjoyed being at the top of the social pyramid. These people rightly viewed the Revolution as a threat to very station and way of life.

The American Revolution unleashed a wave of radicalism that threatened this hierarchical view of humanity. The poor, marginalized, and enslaved were unsurprisingly willing to take a more literal reading of the Revolution's more egalitarian rhetoric. During the war, the elites who worried about abstract concepts like Parliamentary tax policy needed the support of the lower and middling sort that chaffed at the concentration of wealth and property in the hands of a small minority. This translated into state constitutions that were generally pretty democratic - most offices were directly elected, terms were short, and legislatures were large. Some were outright radical: one of Pennsylvania's constitutions (they had several during the war) allowed for universal male suffrage, and New Jersey's granted property-owning women the right to vote.

During the period of the Articles of Confederation (1783-1787), the Revolutionary elites were generally horrified by the actions of these democratic state governments. Corruption - which they saw as the lower sort using political office to improve their financial situation (as opposed to good government, where the elite used political office to improve their financial situation) - was widespread. The poor and uneducated seemed to flood into office and either demand the same respect as the elite or flaunt the idea of respectability altogether. Perhaps most frightening, democratic legislatures changed laws on paying back debts, allowing borrowers to pay back their lenders (in lieu of a real banking system, this was generally the monied elite) with goods and services rather than cash. This threatened to deplete the elite's, and thus the nation's, cash reserves and lead the country to financial ruin.

To curb these democratic excesses and correct the inefficient, ineffective nature of Confederation Congress, the elites called for a constitutional convention in 1787. The document they devised was remarkably less democratic than nearly anything produced during the Revolution. Only members of the House of Representatives would be directly elected. Senators and electors to vote on the President would be selected by the upper houses of state legislatures, and federal judges would be appointed by the president. This was a system meant to resist the whims of the mob. While it was not entirely successful (Hamilton, the Constitution's greatest proponent, said shortly before his death "this American life is not for me" when reflecting on the culture of the country in the early 19th century), it did create more political, financial, and social stability than existed in the turbulent post-war years.

The kind of loyalists who came back and were in a position to re-enter public life enjoyed the social protections the constitution and its supporters, the Federalists, afforded them. This leads us to our next point.

Economic ties with Britain

The economies of what were called at the time the Eastern States - those we now call New England - depended on maritime trade. Despite the loss of fourteen of their American colonies (the British had to surrender Florida to Spain), the British Empire remained, by a considerable margin, the richest economy and largest market in the world. Its Caribbean colonies were still the most natural buyers of American timber and grain, and Americans still preferred British luxuries to everything except Chinese imports. Partly because the Federalists were strongest in the northern and eastern states and partly because they were the governing party, they looked for ways to reestablish normal trading relationship with Britain. This ultimately took the form of the Jay Treaty, an unpopular measure that did a great amount of good for the country.

Many of the Loyalist families that had gone to Canada and England after the war got involved in the merchant trade; with buying property largely off-limits, establishing shipping concerns between Canada, Britain, the Caribbean, and eventually America was a solid investment. Reestablishing social and trade ties with these people was in the economic and political interest of the Federalists, so Federalist politicians led the charge in removing legal restrictions on returning loyalists and generally doing what they could to integrate them into society. In New York, people from the Colden, Delancey, De Peyster, Dyckman, and Robinson families - members of all of which had served in or in support of the British military during the war - became respected merchants in New York City and the Hudson Valley. These families were generally thrilled to return to America, having never felt truly at home anywhere else.

Loyalists and their relatives provided Americans an easy and quick way to reestablish trade to the British Atlantic. For the most part, they shared ideas with Federalist politicians about how a republican society could most successfully function - with power in the hands of the educated, monied elite. By the 1820s, many of the most prominent Loyalist families had members living in the United States.

Sources

Woody Holton, Unruly Americans and the Origins of the Constitution

Maya Jasanoff, Liberty's Exiles

Valrie McKito, From Loyalists to Loyal Citizens: The DePeyster Family of New York

Philp Ranlet, The New York Loyalists

David Waldstreicher, Slavery's Constitution