The 61-year-old recalls how those involved in moving the two cases, which were "bursting at the seams", had acted casually, been in no hurry and even "chuckled" at times. He saw three people but is convinced a man pictured in a TV police appeal was not among them.
Mr Malone said: "After a few minutes we noticed a man and another man - a black man and a white man - carrying a suitcase across the street right towards us.
"They were struggling with the weight of it. I actually thought they might drop it in the middle of the road.
"I thought about going to help them, but something made me stop.
"And so they came over and put the suitcase right by our feet.
"I said to them - 'That looks really heavy, what have you got in there, a body?' - jokingly like you do.
"We were feeling good, happy, so I made a joke and they didn't reply.
"Then they just left it by us and they walked back across the street.
Giles Malone has spoken of his horror following the grisly discovery on Clifton Suspension Bridge in Bristol, describing it as "sickening and chilling".
The 61-year-old also recounted how those involved in moving the two suitcases, which were "bursting at the seams", had acted casually, been in no hurry and even "chuckled" at times.
They had just watched England's semi-final victory over the Netherlands and were waiting for an Uber cab feeling "very happy" near The Mall pub, a short distance from the bridge.
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Officers have been in contact with the family of missing man Jack O'Sullivan to "inform them of the incident" but said "no parallels are actively being drawn".
The Grade I listed landmark, which spans the Avon Gorge, was designed by noted Victorian engineer Isambard Kingdom Brunel and opened in 1864.
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