The so-called backpack or suitcase nuke never really existed as something that the average Joe could haul around with relative ease, ie. carry it like a suitcase in one hand.
Been down the rabbit hole reading about some of our past nuclear weapons designs. Turns out the US did in fact have a brief case sized nuclear weapon designed to be carried by one person. I present the Special Atomic Demolition Munition (SADM):

From Wikipedia: Production of the B54 Mod 1 SADM began in August 1964. The weapon was 12 inches (305 mm) diameter, 18 inches (457 mm) long and weighed 58.5 pounds (26.5 kg), and included the warhead, fuzing and firing system with a mechanical timer, ferroelectric firing set and a sealed housing. The body was constructed with aluminium forgings and moulded fibreglass, and foam-rubber insulation was used between the warhead and case. Dials were illuminated with a tritium-phosphor paint for easy night-reading. A housing for underwater emplacement was provided which included external controls
It used the same warhead that was designed for the Davy Crocket which was essentially a nuclear tipped bazooka:

Depending on the mod, the yield was between 10 and 1000 tons of TNT. It was in service or it's variants until 1979.
Upon further reading, the US actually also had a tested and deployed true three stage fusion bomb called the B41:

The B41 was the largest thermonuclear weapon every developed and fielded by the US. Also from wikipedia:
"The B-41 was of the usual long cylindrical shape. The nuclear fusion warhead was of the Teller-Ulam type and used a 40–100 kt (170–420 TJ) implosion type nuclear fission primary (reportedly based on the Smokey TX-41 shot of Operation Plumbbob)[2] fueled by HEU to trigger the lithium-6 deuteride fusion fuel. The Y1 version, the third ("tertiary") stage was enclosed in a uranium tamper.[1]
The B-41 was an example of a fission-fusion-fusion-fission type thermonuclear weapon, or tertiary stage bomb. The additional tertiary fusion stage, compressed by a previous fusion stage, could be used to make a bomb with yields as large as desired.
The weapon was 12 ft 4 in (3.76 m) long, with a body diameter of 4 ft 4 in (1.32 m). It weighed 10,670 lb (4,840 kg). It was carried only by the B-52 Stratofortress and B-47 Stratojet. It could be deployed in free-fall or aerial (parachute) configuration, and could be set for airburst, groundburst, or laydown delivery.
The B-41 (designated Mk-41 until 1968) entered service in 1961. About 500 of these weapons were manufactured between September 1960 and June 1962. The B-41 was progressively phased out of service beginning in 1963, superseded by the B53 nuclear bomb. The last B-41s were retired in July 1976.
During its operational lifetime, the B-41 was the most efficient known thermonuclear weapon in terms of yield to actual weight, with a 5.2 megatons of TNT per tonne (22 petajoules per tonne) ratio (based on a 25 Mt (100 PJ) yield). Its blast yield was 25% to 50% that of the AN602 Tsar Bomba, which delivered a blast of 50 or 100 Mt (210 or 420 PJ), depending on its own configuration as a clean (lead encased) or dirty (uranium encased) bomb. However even at the Tsar Bomba's theoretical maximum yield of 100 Mt/t (420 PJ/t), it would still only achieve a yield to weight ratio of ~ 3.7 megatons of TNT per tonne (15 petajoules per tonne), thus the B-41 is the most efficient, highest yield to weight ratio, weapon ever created.[3][2] However, since neither full yield versions of the B-41 nor Tsar Bomba were ever demonstrably tested, the B-41's high efficiency is merely theoretical; the most efficient tested and proven nuclear physics package is the W56."
Seems like many ideas about what is possible and what actually happened are in error.