Sam takes an instant dislike to Strider when he sees him in the inn at Bree. He is 'that fellow'. This rises to an earnest desire to batter him when he lays rough hands on his beloved Frodo. Even when they accept his protection Sam keeps up a lively criticism of Strider's decisions, bawling 'What are you doing?' in an American accent when Strider sends Frodo off with Arwen into the night. In the book, Sam even draws his sword on Strider, standing over Frodo. For a king, even one in exile, Aragorn takes this quite well, after a bit of initial huffing. He never tells Sam to shut up, as Faramir does. If he can't win over a gardener what chance has he with a kingdom? Not only are gardeners held in high esteem in the Shire, as Faramir observes without irony, but Strider soon learns that it is the way of hobbits to be direct and outspoken. They make eye contact with anyone, however great, and speak fearlessly even to kings.
But perhaps Strider - and to the end Sam calls him Strider, even when he knows who he really is - senses as Gandalf did with Gollum, that Sam has a part to play in it all. Aragorn, with his lineage, has something of Gandalf's perception.
But Sam has perception of his own. Lower in class than Merry and Pippin, he has more than just stoicism and common sense. He has a keen sense that warns him of things even before the great ones know. At Rivendell he takes a furtive look around before approaching Frodo about going back to the Shire. He does not know that even at that moment he and Frodo are being watched and discussed by Elrond and Gandalf, but he senses some great event is being prepared and his Frodo will be caought up in it. He has the working class belief that they might be dumped on. As they are, even though Sam understands as well as anyone the need for the mission. But this understanding has to compete with his fierce desire to protect Frodo.
Sam is more than just Frodo's gardener. Flashbacks in the book recall him drawing the curtains in Bag End and waking Frodo up. He is nearer to a manservant, what the English call a gentleman's gentleman. But even long before, when Sam sweated at trimming Mr Bilbo's hedge while Frodo read in the shade and dreamed of adventures, the one loved the other.
However, as his enemies soon discover, Sam is no slow stupid hobbit. Mr Bilbo 'learned him his letters', as Hamfast his father said, hoping no harm would come of it. Sam is a poet, learning old lays from Bilbo and making up some of his own. It is from these that he knows well enough the history and nature of the enemy. He has an un-hobbitlike yearning to see elves, the mention of which made him eavesdrop that fatal day in the Shire. And the Elves honour Sam even in his own right, as gardeners deal with the earth they cherish. In the book Galadriel allows Sam to look in her mirror as well as Frodo. It is the the Elves of Gildor, amused by Sam and his devotion to Frodo, who elicit from him his promise never to leave his master.
Most hobbits are poor sailors, so when they get ouf of the boats near Amon Hen Sam slumps against a wall, tired and miserable. He does not notice Frodo slipping away. When Merry asks of Aragorn, with a typically hobbitlike directness and cheeky stare, where Frodo is, Sam leaps up. He suspected Frodo was thinking of doing something like this; he even had doubts about Boromir. Now he can't believe his own stupidity in letting him slip away. When he returns to the shore and sees Frodo already far out the rejection is more bitter than death. Terrified of water he would sooner risk drowning than accept it. When Frodo hauls him into the boat his look of reproach and grief must cut Frodo to the heart but he cannot tell him it was for his own good. Where Frodo is concerned, Sam does not think of his own good, so it would not have been an argument anyway.
In the book the last thing Aragorn says to Sam as they dash off into the woods to look for the others is 'follow me'.
But not even a king could take Sam away from Frodo.