how close together can screws be before weakening a joint
Western Woods Products Association and West Coast Lumbermen’s Association have produced tables and charts based on “stress” for wood fasteners in shear and withdrawal in various species of wood. 

The values are based on the diameter of the fastener and if it is in “stress” parallel to grain or perpendicular to grain. 

So, for wood to wood connections (the spacing is closer for metal side plates) it is: 

For PARALLEL to grain loading: 1) center to center along the grain is 4 Times it’s diameter, 2) row spacing is 3 Times across the grain (parallel), 3) edge distance is 1.5 Times , and 4) end distance (in tension) is 7 Times diameter and when in compression it can be 4 Times diameter...and when installed with less, it’s certain to split the wood.

For PERPENDICULAR to grain: 1) center to center across grain is 5 Times diameter for fasteners with a slenderness ratio of 2 and 6 Times diameter for fasteners with a slenderness ratios between 2 and 5, 2) row spacing is 4 Times diameter, and 3) edge distance is 4 Times for stressed side and is unimportant for opposite side. 

There’s a formula for calculating STAGGERED spacing (and they can be closer together when staggered) but it’s too hard to calculate, so just know that they can be closer if staggered. 

So, to answer your question, yes it does matter and there’s a way to determine the value if you’re Einstein.