United airlines baggage charge, will i be denied checked baggage?

I recently booked an international flight from Edinburgh to Newark, without realising there's a 60 dollar baggage charge for each way, i'm happy to pay this upon checking in

My concern is that at the airport they may possibly tell me there isn't room for my suitcase, has this ever been the case before? I can't even call the airline due to all their offices being based in the US

Of course you can call the airline.

No, you will not be turned away for trying to check a bag.

They might charge u more if it weighs more than what is expected

You can still check the bag when you arrive at the airport, and pay for it then. That's not a problem, and happens often. You, or your bag, will not be turned away.

You can pay when you check the bags. You won't be turned away.

For United, the fee is the same at booking or check in with the exception if the bag is oversized or overweight. It would be extrenely rare for a bag not to make the flight. I put it that way because if you check the bag whether you pay for it or it's included in your ticket, they will get the bag to your destination one way or another. If the plane is overweight, they may move some bags and or passengers to another flight.
Really, the only reason your bag would be denied is if YOU'RE LATE to the airport. United Airlines requires you to check your bag 60 minutes before an international flight.
When you check in online starting 24 hours before the flight, you can pay the fees but you still have to check the bag 60 minutes before.

Are you sure they charge on an international flight? Delta allows a free bag. You can pay when you check in online 24 hours before your flight if you want to.
I tried to look this up, but the United site shows both the first bag free for an international flight in economy AND a $60 charge in economy.

I have never heard of any plane's luggage space being so full that a passenger's bag is refused.

Don't worry about that for a second.

There's little chance of you being refused your checked luggage. You can pay the fee through the manage your booking, at the airport, or if checking in online. You could be liable for extra fees if you go over the 23 kg allowance per bag.

They won't turn down an opportunity to let a passenger pay for something.

My concern is that at the airport they may possibly tell me there's not room for my suitcase.

A real concern for one in ten thousand. On the rare occasion when the plane is full it is full.
You baggage would go next available method.
It happens on occasion. Does it happen often? NO

Suggest you worry about getting to the Airport on time and not packing your luggage to bursting capacity.

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