Wikipedia says they were 14% of the population in 2012. Yet they basically run the country. The Prime Ministers and other government leaders, billionaires etc. I can't find a definitive answer on this but even the Royal Family is at least part-Chinese. They look Thai-Chinese to me.
How did this come about? I know some Chinese immigrated and worked their way up and then more came and they assimilated well. I'd like to learn about this on a deeper level. I'm specifically interested in why the Thai's have allowed this to happen and don't seem to care.
It's not a perfect analogy but it would be like if the United States went in 200 years from the status quo to being 14% German-American, including 90%+ of the Presidents, Congress, Senators, Governors, Fortune 500 CEO's, and billionaires. I can't imagine if that happened the other 86% of us would just think that's normal and fine.
The Overseas Chinese are a classic example (like European and Middle Eastern Jews) of "middlemen minorities". See a longer answer here about middleman minorities and here as well.
But as a distinct, market-dominant minority group isn't the only way Chinese culture exerted influence in Southeast Asia. It's also worth keeping in mind that just as England at various times looked to Christianity, Rome, and France for "civilization" in addition to domestically developed culture, much of Southeast Asia looked to other parts of the world for "civilization"--at various point, Buddhism, Islam (less so in Thailand), India, and of course China. There have been periods where the English bureaucracy was disproportionately French influenced, for instance.
There was also less clear a sense of a boundary between "nations" in most places before the 19th and 20th centuries, and less of a sense that "(ethnic) nations should rule themselves". See here, here here, and here. The idea that there were states that should only contain primarily one ethnic group and that these should be ruled by legitimate representives of said ethnic group seem to date to the colonial period in Southeast Asia. Benedict Anderson, probably the most famous Southeast Asianist in academia, dates this period of national conciousness to mass literacy. Before that, the Chinese might be a different ethnicity from you as a peasant, but that didn't mean that people on the otherside of the country or the royal family were necessarily the same as you. It's worth remembering too that even in European and Middle Eastern countries, the royal family by the 19th century was more often marrying a person from a different country than a local person of the same ethnicity.
Lastly, I think some of those numbers (particularly in politics) are exaggerated. "Some Chinese ancestry" is not the same as being Thai Chinese. Most American presidents are distantly related to English royalty, for instance. Obama, Clinton, and the Bushes all do have some German ancestry (I didn't look back further).