The speaker is correcting a misunderstanding. Someone seems to think the crying stopped because the pain did, but the speaker insists it only stopped because the tears ran out. The grief is still there, dry and permanent, and the repeated "for the record" and blunt "Period" give the voice a firm, almost defensive edge.
The poem argues that loving someone deeply is a kind of trap. The loss is described as a noose that has finally been cut, but being freed doesn't feel like relief. The speaker has lived on a "tether" for so long that standing alone feels like learning to walk again, and the freedom becomes something they drown in. Each stanza ends with a string of similes, and the recurring image of the candle burning oxygen, then smoke, then drying wax, suggests something slowly being used up. The mood is bleak and stubborn, with exhaustion sitting underneath the insistence.