Since increasing tear height and shot speed lowers tear falling speed in order to adjust Isaac's range, increases to either stat will decrease the familiar's range, and decreases to either stat will increase the familiar's range.
Notes
Familiars that follow behind Isaac have a certain priority in how close their position is to him over other familiars, with Fate's Reward having 5th / 7th priority.
Synergies
Flat Stone: Familiar's tears will travel very far and then bounce once, traveling up and hitting the nearest wall.
Haemolacria: Will fire tears that burst into split tears. Does not affect fire rate.
Ipecac: Will fire explosive tears. Does not affect fire rate.
Lachryphagy + Brimstone: The tears fired by the familiar will eventually explode in a star-like pattern of Brimstone lasers if they don't hit anything.
Interactions
Following tear modifiers do not affect Fate's Reward, and the familiar will only fire normal tears: