However, she added that they may not need new powers as "they do have wide-ranging powers, but don't always use them".
The government has said it valued parish councils and encouraged them to work with other tiers of local government.
Weaver, who is now the chief officer for the Cheshire Association of Local Councils, said: "I think perhaps there is some work to be done in supporting and helping our councils to understand what powers they do have.
"And how they might use them going forward in this new world - where we are beginning to look quite seriously at proper devolution down to parish council level."
She said there was a "place for everyone in the parish council sector".
After her moment of fame in the media spotlight, she said people still recognise her.
"I definitely look back on it fondly. Do I get recognised? Yes I do in the oddest of places but they never ask me," she said.
"They always ask somebody else if that's Jackie Weaver."
