Posting mostly because I think I can help you narrow down what abilities trigger the "glitch" weather. Also putting a disclaimer that I have no clue how Nintendo actually codes, but am making an inference that weather and similar effects (Trick Room and co) are all stored as part of a giant conditional statement of some sort due to things I'll discuss below. If anyone knows how Nintendo codes and can verify that they do something completely different (and, unless I'm missing something, rather nonsensical) to determine field weather, you can feel free to ignore this.
It's most likely caused by bad coding that resulted in some of the variables that determine the different aspects of how Pursuit works not being scoped correctly, or by giving Pursuit access to functions or objects on a programming level that it shouldn't have access to because they were in a rush job to finish patching Pursuit for the Platinum release. Either that, or the coder was just lazy. However, it is definitely a "glitch" by all means, because it's accessing the conditional statement that determines what effects are active on the field.
This explains why there is a very specific order (Rain -> Sandstorm -> Sun -> Hail -> etc), because that would be their order in the conditional statement. This also explains why only certain weather effects can clear each version of the "acid" weather, because anything that's not on the highest tier of "acid" weather or higher already has its variable set to "true" and is stopping itself from being reset. I also noticed Trick Room (and probably Gravity and Uproar as well) cannot reset this condition, despite being higher tier. This is probably because the conditional statements that launch those field effects don't include a clause that resets weather, further showing that this is accessing the nest of code that influences the field in some really crooked way.
What this does mean, though, is that process of elimination can easily determine what will most likely influence this glitch and be present on the tier lists: attacks that influence the entire field in some way and do not target, aka pure "weather" effects. This eliminates Wrap-like moves, Aromatherapy-like moves, etc. from the equation simply because they are either stored in independent codes, or the conditional structures that trigger their lingering effects (such as Wrap damage) are different from the ones that determine weather.
This also explains a lot of how it interacts with abilities, such as how all the positive aspects of each weather seem to stack with the negatives of those weathers being ignored (things like Swift Swim as well as things like Solarbeam or Thunder). Since all the variables for the weathers present in "acid" weather are set to "true" up to the last one visible, and the positive weather is most likely looked for first with the effects of the negative weather being contained as part of a nested "else-if" or similar conditional, all pokemon, stats, and abilities are probably noticing the weathers they like are there and simply ignoring the others are present. This means that in "acid" hail, Thunder, Blizzard, and Solarbeam will all *most likely* get their accuracy boosts / charge time decrease simultaneously, even though other weathers to contradict that boost are there. For anything lower than "acid" hail, all positive effects up through the last "acid" weather would apply, and all those after it would not because that weather is still set to "false".
The damage is probably also caused by a different function that is called by the end weather animation when Sandstorm or Hail are present. This explains why all weathers will inflict damage as each animation ends, but not why its accessing the name value of the Pokemon's ability to do so. The only thing I can guess from this is that the function is doing the 6% damage, but is calling the message displayed for when a Pokemon is hurt by Solar Power or similar self-damaging abilities instead. They probably contained the message for abilities such as Solar Power (as I'm sure more than one ability damages its owner) in a function or class or something, and have it printing " (Pokemon) was hurt by its (Ability) ", with (Pokemon) referencing back to your Pokemon's name and Ability referencing to the name of your Pokemon's Ability, respectively. This explains why Pokemon lacking abilities display a -, because - is probably the Ability string's default value as a safeguard to stop crashing during shoddy hack jobs or during testing phases. I honestly can't explain how they managed to pull this off without some really messed up coding due to the fact I don't know the code used in ROMs, but that is what's most likely happening. The message display probably also controls what Pokemon are immune to damage, which is why "acid" Sandstorm doesn't damage Rock, Steel, or Ground types but "acid" Sun and onward damages everything without an ability override, because its instead most likely referencing the text control for damaging abilities, which has no immunities to send back.
The reason that Pokemon with Ice Body does its Heal / Damage thing can also be explained by this, most likely. Ice Body and co are probably set not to call the heal message if the Pokemon has full HP. Since Ice Body won't override the weather due to that, and there are no immunities being sent back by the text display, the Pokemon is probably noticing the weather and being damaged by it, because no immunities are being returned. When Ice Body can perform some healing, it overrides the damage display message via the positive-negative conditional structure I talked about earlier and heals the Pokemon for that instance of weather, because the "Hail" variable is set to "true" during "acid" Hail and onwards. While it wouldn't hurt to test, other abilities such as Rain Dish are likely to be structured and will work the same.
I think that covers almost every aspect of the "glitch" from what I can tell of these threads. Hopefully, this will help with testing it in game by narrowing down what needs testing, and help the people who actually want to tear apart a ROM and find this thing have a better idea of where to look for it, granted Nintendo actually did what they seemed to have done with weather and made it a conditional statement. At least, thats what this "glitch" really seems to be from a technical side of things, without actually going into the ROM and tearing it apart to find it first hand. I'd do some testing to back this stuff up, but I don't have a means of getting a copy of Pokemon Platinum to test with, sadly. Like I said though, hopefully it'll make other people's testing easier.
Also, hi.
