A family statement said: "Bob was an extraordinary man, and to the family not really because of the amazing age he reached.
"A role model to us all, he lived his life interested in and engaged with all kinds of people from across the world.
"He viewed everyone as his brother or sister and believed in loving and accepting and caring for one another.
"He had many, many friendships and read and talked politics, theology, ecology and more right up until his death.
"He also cared greatly for the environment.
"The second bedroom in his flat was a workshop, filled with furniture, windmills and puzzles he made and sold in aid of charity, often from bits of wood pulled from skips.
"We are so grateful that until the very end Bob remained our witty, kind, knowledgeable, conversationalist father, grandfather and great-grandfather, and we will miss him greatly."
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Weighton's celebrations for his birthday in March were tempered by the Covid-19 lockdown.
He said the "world is in a bit of a mess" with the ongoing pandemic.
The conscientious centenarian turned down a birthday card from the Queen, saying he had received at least 10 from her already and didn't want taxpayers to pick up the tab for another.
Weighton previously told the BBC: "I think laughter is extremely important.
"Most of the trouble in the world is caused by people taking themselves too seriously."
He joked that the secret to his longevity was "to avoid dying".
He is survived by his children David and Dorothy, 10 grandchildren and 25 great-grandchildren.
