The most successful stalls in the current Standard metagame tend to be heavy stall.
I don't really agree with this. The most successful stall teams tend to be essentially tanking bulky offense with slightly more emphasis on entry hazards and defenses with a forretress or skarmory thrown in. Pokes like Hippowdon and Blissey are seeing usage drops in favor of stuff like swampert and cursetar that are more capable of dishing out hits. It tends to be a better strategy these days to use things with high attack stats and good defenses to tank hits and OHKO back rather than simple walls.
I think that the simplest way to explain the difference between tanking and heavy stall would be to look at the difference between obi stall and ipl stall. In obi stall, nearly everything self-recovers and simply walls threats until they decide to switch or until they are worn down by weak stab moves. IPL stall is almost always able to tank a hit or two and OHKO opposing threats (especially ones that can stat-boost like Mence and Infernape, but at the price of lacking reliable recovery on most of the team.
In obi (heavy) stall, there is also much more importance put on spreading out the entry hazards onto multiple pokes. IPL simply puts most of his hazards on forretress and puts up spikes and tspikes as they switch out of it. IPL also focuses more on general tanking rather than rely on skarm/bliss to take respective physical and special hits. His members are EV'd to have 60% physical bias rather than full physical or special bias.
Tanking stall is generally proving to be more effective than heavy stall in this metagame, and I think this is because heavy stall is finding it hard to put up hazards with rampant uturn abuse, meaning that tank stall is better because it can hit things hard as they switch in rather than relying hazards to do the damage. the rise in Rotom usage in platinum has also prompted stall to use harder counters to it, which may explain the dip in blissey usage in favor of curse tar.
Also, I agree completely with what iKitsune said about stall.


