I have hopes, but it likely depends on the airline.

Had an empty flight with Singapore Airlines right after Christmas and they didn't.

This is British Airways so we'll see.

If you ask, they'll almost always say yes. Something like, "Hey, I noticed the flight is mostly empty. Would it be possible for me to get a complimentary upgrade to one of the empty first class seats?"

They're losing millions of dollars every week. Will they still be eager to say yes?

1. The steward(ess) isn't losing millions of dollars every week.

2. Does it cost them significantly more to seat you in a different location? I'm asking, I genuinely don't know.

I wouldn't mind economy service if I still get the first class seating. So zero cost for them.

I'd take any kind of upgrade to be honest.

Right now I'm in premium economy as for some reason the ticket was cheaper than economy.

The question is if the stewardess cares as much as the airline.

Realstically speaking there is virtually no difference in service for them.

Assuming that I get the usual economy food and I'm really the only person on the flight.

Unlikely. There are different crew for different cabins. When a flight departs without anyone in first, for example, they don't normally bump people up to fill it they redistribute crew into the main cabins.

Now, if you fly regularly and have some miles status with that airline you can request all sorts of things. The gate agent has a lot of leeway in that regard.