We can debate if a weaker dollar would have a overall positive or negative impact, or on whom it would have impact on.
However, it would mean higher interest rates. Bonds that have been issued would go down in value but we don’t care about those – we care about the new bonds that will be issued.
As you pointed out, a weaker dollar means more expensive imports, more expensive imports means higher inflation, and higher inflation means a higher interest rate.
Also, a weaker dollar reduces the return of US bonds held by foreign owners, so they would demand a higher interest rate to compensate.