"Strongest" and "Heaviest" may not go together. Though many think of tons-o-latakia when they think of heavy, the stuff actually falls pretty low on the strength-o-meter, despite the weight of the smoky goodness. And, more isn't necessarily going to seem fuller, either.
When there's a LOT of latakia in a blend, the palate becomes fatigued pretty quickly. While the first few puffs may deliver a boatload of flavour, the ensuing attenuation of the senses will tend to make those flavours seem smaller over time. Paradoxically, orientals can increase the apparent weight and intensity of the smoke, despite being fairly mild on their own, and virginias can help to prevent palate fatigue because their sugar content tends to refresh and reset the sensors. So, something with 50% latakia (quite a lot) can seem fuller, heavier and stronger than a blend with 80% of the stuff, which can be dull and monotonous, and ultimately, thin tasting.
Another thing to consider is personal chemistry and preference. I know some blends that I'd consider very full that others think of as light or medium, and vice versa. What's heavy for one might be a lightweight to another.
That said, there are some contenders mentioned that are probably almost universally considered heavy, if not strong. For the heaviest AND strongest, I'd have to go back to some blends that are long lost to the ravages of time. The old Dunhill Nightcap would fit, as would the original Craven Mixture, and a few others. These were blends that I had to smoke carefully in small pipes in order to avoid a nicotine knockout. Later examples were somewhat tamer…
In my own range, Abingdon might serve, or Charing Cross. These are not particularly strong, but they are fairly full. Quiet Nights isn't as full, but seems a little stronger. Getting both in one package isn't so easy.
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