What you are missing is "leverage", which is the typical case for real estate purchases. Buyers usually only put a percentage of the cash down, not the whole amount. So instead you have something like this:
Year 0: Buy $100,000 house for 10,000 down. $10,000 equity, $90,000 debt.
Year 5: Sell house for $300,000. Even if the debt was not payed down and ignoring fees/expenses, that means you have $210,000 in cash at sale. 300,000 sale - 90,000 debt = $210,000, so 200,000 profit out of your starting 10k in cash.
So, let's say the $150,000 house also tripled to $450,000. When you first bought you could only obtain a $90,000 loan with your $10k cash, but at the same 90% loan-to-value ratio $210,000 could now secure you a house costing $2.1 million. That's leverage in action. You could also put all the cash down on the expensive house and it is now available to you with a ~50% loan, whereas previously it could not be purchased at all.
Note that the "upgrade" still increases your debt and overwhelms your equity, so you go from being up 200k after the sale to being in debt by millions after the purchase, and it also increases your expenses. This is why this is a dangerous game. If your plan was to "upgrade" again at year 10, or at least cash out and enjoy being a millionaire, what if house prices fell, flat-lined, only grew very slowly - and something happened to your income and you couldn't keep up those huge debt payments?
If things go as planned, though, leverage is what delivers the theoretically big upgrade. House prices grow by a percentage of their value - regardless of the percentage of the value you have in equity at the beginning, and regardless of how big the theoretical loan is. If housing prices increase faster than the yearly interest (which is certainly not guaranteed!) you pay on the loan, every year is a paper profit and your buying power increases.
In fast-growing housing areas, this was what created the "property ladder". You bought a house, and in a few years it was worth vastly more - and your income was probably higher now, because the economy was booming. So you bought a bigger, fancier house and in a few more years sold that too (or just refinanced) and bought another. 20-30 years of regular living produced millions in profits once it was time to sell the great big house, downsize, and enjoy your retirement. This has lots of assumptions - from higher income to fast growing housing markets, to employment stability, ease of selling or refinancing, etc. Don't assume what works on paper necessarily will work in practice!