SE obvious has a history of increasing the iLVL every couple of major patches (for good reason). But with secondary weights as they are at 60 I'm not so sure they will do the 20 iLVL jump this time. They will increase it clearly to give incentive for the new raids, but I don't think such a large increase is needed anymore:
1. The original jump in 2.2 was due to the max weapon increase in 2.1. In 2.0 the cap was 90 for everything. In 2.1 they changed it so that the weapon was capped at 95. When they released 2.2, they had 95 weapons, but realizes this was a bit close considering they also intended to add intermediate raid weapons (which is a bit different than tome weapons now).
2. Since they already had 95 from the previous patch and added entry weapons (95 weapons from levi), intermediate raid weapons (100 weapons from unidentified allagan tomestone), upgraded entry weapons (100 weapons from levi) they may have felt that the levels were too close to encourage the last tier of weapons and they had made the final weapons 115, since the upgraded intermediate raid weapons at 110, possibly to add a 105 weapon later (wonder why that didn't pan out...). It of course came to pass that in 2.3 they added more 95 weapons (crafted) and 100 weapons (ramuh) and didn't let any weapons catch up to the raid weapon. Of course I'm intentionally ignoring the relic here since those had no influence on the release of other weapons due to them always being behind the raid weapon. IIRC, 2.2 only had animus, which was 100 and 2.3 added Novus, which was still behind high allagan.
3. Since we don't have an influx of weapons from the previous patch, the weapon cap is at the gear cap, and the raid weapon is the only max level weapon at the gear cap (since they reversed how they handled tome weapons) there's no need for the jump. 20 iLVLs. Right now, they only way a person has a 210 weapon in their possession is the final raid (no one right now has a 210 anima in their possesion). Since we no longer needed a drop from the raid to get an intermediate weapon and they separated upgrade items from the main gear and weapons, there is no significant creep and the vast majority of people do not have a max level weapon. Note this time that we don't have a plethora of weapon choices any more for weapons and they no longer have the problems of splitting secondaries to make weapons diverse.
4. Raid gear progression is now fixed, rather than random. In the 3 sets of coil, you can get anything barring the weapon in rather inconsistent set of floors. Alex is fixed in the sense that they now control what contribution gear will have because all of the stronger pieces drop from the later floors. The inclusion of Alex normal has made this even more prudent, as now you can get an entire set of entry gear before you hit the real raid, so expected iLvl is more clear.
Therefore my predictions of 3.2 (speculation of course) based on SE being consistent with reasoning and SE actually doing what they mentioned in the previous live letters:
Raid gear 220, raid weapon 220, materia slots
Alex normal gear 210
Entry tome gear 215 no upgrades, no entry weapon
Entry weapon 215 as primal weapon
Relics increase to 215, materia slots
Crafted entry gear at 210, obviously materia slots
For 3.3:
Relic increase to 220
Crafted weapon at 215
24 man gear at 215
(Diadem intentionally omitted)
Now I know what you are thinking: "There's no upgrade item at all or tome weapon!!"
The upgrade items were only introduced because they needed a sense of weekly progression of gear to measure expected completion times. The tome weapons are actually a 1 patch thing only added for heavensward (all the other "tome" weapons required a raid drop"). With the levels being so close, the weekly tome gear is as progressive as it gets. Since they will probably have a new primal, the primal will drop the entry level weapon for the new raid. Unlike patch 2.2, we don't have the issue with only 1 weapon at 95, being an outlier. I'm actually sure they intended to have levi weapons at 90 if the kept allagan at 90 in 2.1.
Conversely, our highest tier of gear is equal to the gear cap and they may choose to have the primal drop at 210 weapon. But as this will get largely ignored by those already with 210 weapons (see Ramuh Ex in 2.3) they will make this a step above the previous gear cap. With no need to have a 95-100 upgrade this time to encourage people to complete it (like leviathan) they have no need to increase the level of the entry weapon from 215. Since the entry weapon is static and they also have a problem with itemization (accuracy is removed so only 3 unique weapon stat combos can exist, barring which stat is the high/low one) they can make at most 3 weapons. Since the relic and the raid weapon are guaranteed to exist, this leaves them with leeway for only one more weapon. Since they promised to make crafted relevant (but not to overshadow raid weapons to discourage relic or raid) this is the only choice they have left.
Since they have no reason to have the difference that high anymore, they will probably not have a tome weapon anymore, nor upgrade items. But now I know what you are thinking: "So all BiS comes from raid????". Well there's still diadem in the background. I can't make a logical prediction on the gear level since everything SE did with diadem is illogical in itself but I'd put my money on 215 at 3.2 and 220 at 3.3. Alex normal however is the odd ball here, since that in itself is new to 3.0. But as it is, the tome gear eclipses the alex normal gear. They probably want to encourage entry barring ~600 runs of it for a relic step (which will not immediately have much participation in the next step due to the sheer amount of time to do the current ones) of Alex by making it supplement the tome gear for progression. It being 210 is only due to the fact that there can be a way to gear alternate classes in progression without grinding the previous tier. I think the biggest problem with alex normal gear was that it was too far from the tome gear to supplement progression. Keeping the pace that they have now, I'm expecting that they intend for the first full clear to be a bit after a month of release, while the rest trickle in, in the following month.
That said, SE can also do the illogical which is:
Raid stuff 230
Tome stuff 220, upgrade to 230
Alex normal stuff 210
Crafted stuff 200
Relic 215
Which is what they have now. But there's no longer a reason for the power creep and there is going to be a way to supplement gear with materia. Also the lower level will make the current gear a bit more relevant (e.g. relics at 210).