Hi @T1DK, Thanks for sharing the story of your grandpa and the inherited pieces-I found it fascinating! I believe the scoresheet signed by Henrique Mecking is truly invaluable.
About the sets, I'm not entirely sure about the origin of the first set, but the second one looks familiar. I hope the information below helps guide you in the right direction with your research.
The first set, with the tournament-sized pieces have some similarities with Brazilian pieces that were produced by the company Bonatto (from Curitiba), potentially during the 50s to 90s (though I can't say for certain). Bonatto used to craft such sets with the finish that you can see in the pieces: detailed and sturdy pieces, a consistent finish, and a premium look and feel.
The travel-sized set could also be an original Bonatto set from anywhere between the 90s and 2010s, but again I'm not entirely sure. Currently, there's a company called Botticelli that produces some sets that resemble the same designs. They currently offer a travel set featuring a 6.5cm King and a folding board with 3x3cm square, which are very similar to the set you inherited.
You can check out the pieces here: https://www.tocadotabuleiro.com/produto/pecas-de-madeira-para-jogo-de-xadrez-rei-6-5cm-sem-tabuleiro-botticelli-303 and the folding board here https://www.tocadotabuleiro.com/produto/tabuleiro-marchetado-estojo-para-xadrez-c-casa-3x3cm-sem-pecas-botticelli-1468
I've recently inherited two of my grandfathers chess sets. One appears to be a regulation size board with it's accompanying chess pieces. The other appears to be a smaller travel-size set. There is also a chess clock which goes with the set.
For context (hopefully not doxing myself too hard here) my grandfather was relatively skilled at chess - he was 1 of the 4 players to draw with Henrique Mecking when Mequinho came to Compinas, Brazil in February of 1972. Mequinho played 16 players at once and my grandfather was able to end in a draw. None of the 16 beat Mequinho. Afterall, Mequinho is one of the best Brazilian players of all time, and arguably one of the best in the world at certain points. I have the original scoresheet that was signed by Mequinho after they played.
Unfortunately my grandfather suffered a TBI in a car accident when I was very young and he has always lived in Brazil while I grew up in the US so I had very little ability to speak to him about his life at all, nevermind his years of playing chess. He passed away quite a few years ago.
I've attached pictures of the pieces to your viewing pleasure and hopefully some insight from you all.
Thanks for reading!
TL;DR
This is a long shot, but if anyone has information on these pieces, dates, names, manufacturers, etc, I would love to find out more. It has been very difficult to locate accurate information online.