What makes V1 one or two knots less than Vr on this performance table?
$V_R$ is:

FAR 23 (e.g. multi-engine small planes):


  $\geq 1.05\;V_{MC}$ (105% of minimum control in flight)
  
  $\geq 1.1\;V_{S_1}$ (110% of V-stall for a specific configuration)


FAR 25 (e.g. transport jets):


  $\geq V_1$
  
  $\geq 1.05\;V_{MC}$
  
  Must result in $V_2$ before 35 ft height
  
  Must result in $V_{LOF}$ [when the airplane is rotated at its maximum practicable rate]
  
  
    $\geq 1.1\;V_{MU}$ (all engines operative; AEO)
    
    $\geq 1.05\;V_{MU}$ (one engine out)
    
    $\geq 1.08\;V_{MU}$ (AEO, geometry limited)
  


Geometry limited is when there is a greater risk of a tail-strike, e.g., a stretched variant of an airplane (think A321 or 737-900).

So the 1-2 knot disparity in your example can be down to the difference between $V_{MCG}$ and the 105% of $V_{MC}$ or the different $V_{MU}$ speeds. (See below for full text on points 2 and 4.)

To clear any confusion about the Weight:V1 tables such as the one in the question, those tables are not for 1 runway length, those weights are the field limit weight, i.e., each higher weight in the table is a longer runway.

(Twitter) $V_{MU}$ test.



Source: http://wpage.unina.it/fabrnico/DIDATTICA/SPER_VOLO/APPUNTI_3CFU/11.2-TO&amp;LAND.pdf

FAA AC No: 25-7C text:


  
  VR may not be less than V1; however, it can be equal to V1 in some cases.
  VR may not be less than 105 percent of the air minimum control speed (VMCA).
  VR must be a speed that will allow the airplane to reach V2 at or before reaching a height of 35 ft. above the takeoff surface.
  VR must be a speed that will result in liftoff at a speed not less than 110 percent of VMU (unless geometry limited) for the all-engines-operating condition and not less than 105 percent of the VMU (unless geometry limited) determined at the thrust/weight ratio corresponding to the one-engine-inoperative condition for each set of conditions such as weight, altitude, temperature, and configuration when the airplane is rotated at its maximum practicable rate.
  


(Emphasis mine.)