This is what happens when I rewatch The Winter Soldier and spend the whole time trying to work out what Nat is thinking.
Title from The Secret Garden
Warning: Sad. Really sad. No fluff here.

Waverly isn't a small town by any accounts, technically it's a city, but it still makes the back of Sam's neck prickle. He's lived in big cities all his life, so country towns are the complete opposite of his thing. They're not really Steve's thing either, which makes this weird road-trip thing they're on even weirder.

They're only stopping overnight here, on their way to Charles City, so all that really matters is that the motel's clean and they can restock their supplies. There's been a sighting of The Winter Soldier in Charles City, or at least there seems to have been, but all they're really going on is a hysterical blog entry that was written last week. Even if he was there, the chance of him still being there by the time they arrive is close to zero.

Sam is quietly worried they'll never find him, that Steve's running around the country chasing someone who doesn't want to be found. That translates into worrying about Steve, because Steve has tied himself to the faint hope that they can get Bucky Barnes back, even though they both know deep down that Bucky is gone.

They've pulled up behind the cemetery and flattened the map out on the hood of the car to check the route (their GPS is the least reliable thing Sam has ever seen) when Sam notices… someone in the cemetery grounds. A red-haired, female someone.

'Steve, hey…' Sam points her out because Steve's eyesight is better than his, and because he's ninety-nine-percent sure who it is already, he just needs confirmation.

'Hell,' says Steve, 'what's she doing here?' and they're still staring when Natasha stands up, wipes her hands on her jeans, turns and sees them.

They stare at each other, and Sam is reminded forcefully of being caught staring at the guys on the soccer team and hoping to God they didn't realise why he was staring. Finally Natasha looks down, does something with her hands. A second later, Steve's phone goes off with a text.

You might as well come in.

Sam and Steve exchange glances, because how often does your friend (friend?) invite you into a random cemetery?

They find her ten minutes later, staring at a few graves that seem to be a set. One's an old, double plot, the other two are newer. Sam reads:

In loving memory of

Harold Charles Barton

1950 – 1980

Edith Francis Barton

1953 – 1980

"I will fear no evil for thou art with me." – Psalm 23

The second one is a lot more bland, reading simply:

Here lies

Charles Bernard Barton

1973 – 2006

The one Natasha is looking at is the newest.

In memory of

Clinton Francis Barton

1975 – 2014

Dearly beloved

Beside Sam, Steve has gone very still.

'He wouldn't have wanted to be buried here.' Natasha blinks furiously. 'They didn't tell me they were putting him here. I wouldn't have let them.'

'Nat, I didn't realise…'

Natasha laughs. It sounds horrible. 'Where did you think he was?'

'I just though…' Steve shakes his head. 'What happened?' His voice has gone impossibly soft.

'The Taliban don't like American spies.' She's biting the inside of her cheek. 'I was in Italy. I couldn't – I didn't – fuck.'

It's then that Sam suddenly realises who Clinton Francis Barton is. Was.

Steve swallows, and Sam wants to take his hand, hold him close. 'I'm sorry, Natasha.'

'I don't need your pity,' she spits back.

'Do you honestly think I pity you?'

Natasha shakes her head. 'I fooled myself into thinking that maybe we'd both survive. Stupid.'

There's nothing more to say after that. They just stand there for a while, and Sam does take Steve's hand when a single tear runs down his cheek. Sam feels almost like he's interrupting something private, something sacred. He never knew Barton.

Natasha must have loved him.

She walks with them back to the car, and instinctively Sam says, 'you can stick with us if you want.'

Nat smiles at him. It looks painful, but it also looks real. 'Thanks, but no thanks. I think I'm better off alone for a while.'

She walks off before either of them can say goodbye.

I am so, so sorry.

(ps: all I know about Clint's family comes from Wikipedia)