The game keeps track of how many Diamonds you have gained (it doesn't matter how you got them) as a score. When this score reaches certain checkpoints, your support level will increase, earning more "Support Level Bonus". This bonus stacks multiplicatively with the Lineage Level bonus.
On the table below you can see what you can earn for each Support Level you reach.
The Experience and Gold Boosts stack additively with most other sources (Ascension Boost upgrades, Account upgrades, Altar bonuses, Event point bonuses, Guild upgrades, and, additionally for gold, Gold Rate (the upgrade purchasable with gold) and Inferno Bonus), but multiplicatively with the Party Boost ascension upgrade.
At a support level of 7 or above, a player's collected stone will no longer be upgrade-only when leaving a guild.