The sun’s gravity gets weaker the further out you go, the same goes with the Earth. But even back out all the way to Neptune and Pluto, the gravity is still there. The sun can even keep Sedna which at its aphelion of close to 1000 AU, still keeps Sedna from flying away. Does this technically mean that the gravity from celestial bodies extend out infinitely, even if it has a really tiny effect further out?
Does gravity extend out infinitely?
Does this technically mean that the gravity from celestial bodies extend out infinitely, even if it has a really tiny effect further out?
Basically yes, you've got it right. It's a big challenge when calculating orbits in the solar system (everything pulls on everything) and even galaxy evolution and intergalactic dances.
But technically no, the limit being the speed of light. I will not give a technical, general relativity-based answer other than to say that gravitational influence (as well as other fields like electric and magnetic) only extend as far as the observable universe from their source.
Nobody knows for sure how big the actual universe is, so we don't know just how small a fraction of the whole universe the observable part is.