"I should like to save the Shire, if I could - though there have been times when I thought the inhabitants too stupid and dull for words, and have felt that an earthquake or an invasion of dragons might be good for them. But I don't feel like that now. I feel that as long as the Shire lies behind, safe and comfortable, I shall find wandering more bearable: I shall know that somewhere there is a firm foothold, even if my feet cannot stand there again."

carrying the world around his neck

"I see no hope of it now. But I've got to do the best I can."

contrary to a lot of the movie contrived bs (and the movies are my favorite films okay)
frodo praises sam like…all the time in the books. calls him, ‘sam dear, my dear sam, dearest of hobbits, friend of friends, ’ and not once, in the entire journey, does frodo leave him. 

so if he ever gets the opportunity to bring up his friend he’s going to bring him up. not like in a romantic way but like they are terms of endearment, you know? like, it’s such a loving relationship and a really pure kind of love. not in the sense they are in love like sam is with rosie, but they are in love with each other as friends, their friendship is really what keeps them going. 

there really isn’t a moment in the books where frodo does not appreciate sam going the miles he does for him, even though frodo told him not to come for his safety showing how deeply he loves and cares for his 'servant’. 

while he has a substantial bffery with merry a lot in the books, i think to a degree near the end, samwise becomes his best friend, and in a lot of ways like a little brother to him? they have a twelve year age difference, so frodo is often a big brother figure. even in the films he has moments where he’s like, 'don’t look down sam’ or 'come on sam’ and gently puts his arm around him.

so really hearing people say frodo doesn’t appreciate sam or that he does nothing in their friendship is a load of bullshit in my opinion. i mean even in the films where frodo is about to fall off, he considers letting go so sam can make it out of the cracks of doom. that’s the deepest level of platonic love. and that’s why their friendship is so famed, i think. i honestly believe frodo fights as much for the shire as he does for a way for sam to go back to the things he loves. in a lot of ways, to frodo, sam is his hero and that’s why he’s so quick to deny all praise to himself as being a hero himself, when he very well is. 

tl;dr; 
both hobbits are heroes in their own right, and to hate on one and love the other is kind of weird because they are a team-unit, and they don’t go anywhere without each other.