His team-mate Darren O'Neill was beaten 16-7 by Arten Chebotarev of Russia in the middleweight final.
Despite the disappointing ending, it was still GB's best showing at the tournament since 1961, with the team finishing with three silver and two bronze medals (for bantamweights Gamal Yafai and Andew Selby).
Barnes' gold, meanwhile, was his country's first since Paul Griffin in 1991 and Ireland finished second in the medals table behind hosts Russia, with one gold, one silver and three bronze.
British head coach Robert McCracken refused to be too downhearted about his team's final day but was clearly aggrieved by judging that appeared to leave Yafai, in particular, short-changed.
McCracken said: "Khalid was clearly the better boxer and I thought Iain could have had better luck too. But the fact is we have come away from the toughest of tournaments with five medals.
Behind the scenes with Britain's top amateur boxers
"When the disappointment of today is over we'll look back at a great tournament which has proved Great Britain belongs alongside the likes of Russia and Cuba as one of the strongest nations in boxing.
"And the success of some of the young fighters out here - in particular Iain and Gamal - sends out a fantastic message to our development boxers that with work and application they can also make it right to the top."
Birmingham's Yafai, who competed at the Beijing Olympics, appeared to be landing at will with body shots, especially in the final round.
However, the 21-year-old had to wait until the final seconds to register his only point by which time Aloyan, who also beat Khalid in the European junior final three years ago, had victory in the bag.
Bournemouth's Weaver, 20, was undone by the counter-punching skills of Makarov, who pulled away in the final round to take gold.
Liverpool's Stalker, 25, put up a brave fight against Russia's former world and European champion Selimov, recovering from 4-0 down to make it 4-3 before falling away again.
Barnes, an Olympic bronze medallist, boxed a calm and tight fight throughout, building on a 1-0 lead at the end of the first round to go 3-1 up at the end of the second.
Ireland head coach Billy Walsh said: "Paddy is a winner - it's as simple as that.
"He doesn't want to settle for second best and gold is all that he has desperately wanted all along. It's a fantastic achievement and we're all delighted for him."
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