He figured it out..
after Jake turns into a wolf in front of him he realizes anything is possible.
When he saw Nessie he realized it was his granddaughter but couldnt comprehend how it happened so fast.
He decided not to ask questions, because he loves Bella and Nessie so much, and he didn't want to know.

I think Charlie realised that Nessie is Bella's when he saw Nessie's brown eyes, which are Bella's exact eyes

agree with everyone here
and that Bella was looking so pail like all of the cullen's :D he didn't wanted to ask question because Jake turned into a wolf right in front of him, so he knew everything was possible even the same idea with Nessie :D hihi hilarious i would die to see Charlie's face when Jake turned himself in front of him, if they show that into the movie :D

thank you all for that it has helped me thank you