The reason why H is silent in some words and others it is not is due to the influence that French had on English, all of the words you listed Honour, Honest, Heir are from french origin and they don't pronounce the H in most words a notable except being human. Then words like hair are from Germanic orgin and the H is pronounced another. The way I'd suggest going about this is since Portuguese and French are similar if the english word you're trying to pronounce looks similar to the Portuguese word that starts with H you probably won't pronounce it of course there are exceptions like human where its french origin and they pronounce the H and also with habit which is french origin and they don't pronounce the H but English speakers do.

In French, the silent H is called H Muet. It's not a surprise if English also has this. Please note that H as in "Herb" is sometimes silent in American English.