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Great question!
No, the Sun's diameter will expand greatly but it's mass will remain mostly the same, if anything it'll be ejecting significant amounts of stellar matter when it turns into a red giant and will be losing mass.
Mass is what dictates the gravity of a given object. If you replaced the sun with a black hole of the exact same mass, everything in the solar system would retain its exact same orbit outside of those few unfortunate objects that were very close to the sun (much closer than Mercury) when it got swapped out for a black hole of the same mass.
So even though the Sun will eventually swell up into a red giant and eat most, if not all of the inner planets, it's gravity will remain the same despite its massively increased diameter, and its gravity will get weaker as the red giant ejects stellar matter over its relatively quick life. Eventually it'll eject its outer layers, creating a new nebula thanks to the star ejecting all of its outer layers and leaving behind the dead core of a star called a white dwarf. These dead stars are often similar in size to the Earth but typically have a mass close to that of our sun.