[2020] What's the point of loot?

Item affixes do have tiers with higher values. At higher levels items spawn with higher tier affixes on average and items with higher combined affix tiers have a higher level requirement. You can view the tiers of an item's affixes by holding ctrl and alt while hovering over it.

Tiers 1 to 5 can also be crafted using affix shards (e.g. using a dexterity shard on an item with a tier 1 dexterity affix will improve that affix to tier 2 dexterity). Tiers 6 and 7 are drop only and can only be found in end game content.

It depends on the affix. There are many cases where a difference of 2 tiers will more than double the value, but there are also cases where there's a smaller increase.

It mostly depends on how impactful small amounts of a stat feels and how much a stat's relative power drops off with level. For example an added melee physical damage affix approximately doubles its value every two tiers, because you get a lot more added melee damage from your weapon at higher levels and the affix's power needs to increase similarly to keep up in relevance at higher tiers. However something like increased cooldown recovery speed has few sources and doesn't have to keep up with any enemy properties such as health, so 10% increased cooldown recovery speed matters about as much in end game as it does in early game. Consequently the increased cooldown recovery speed affix has smaller increases per tier, so that we can make it feel noticeable early on without it becoming too powerful at end game.