To elaborate a bit more on why this can be confusing, there are several confounding and competing variables in determining relative recoil between chamberings of different calibers. In the SAAMI document mentioned above, we are primarily concerned with how this expression compares between 6mm and a 6.5mm cartridges:
(W_E*V_E + W_PC*V_PG)
where,
W_E is the bullet weight
V_E is the bullet muzzle velocity
W_PC is the powder charge weight
V_PG is the muzzle velocity of the powder gases
Now, V_PG is not only a function of muzzle pressure, but also the bullet's muzzle velocity, a dependency derived phenomenologically for rifles to be V_PG = 1.75*V_E, and the above expression becomes
V_E * (W_E + 1.75*W_PC)
Let's assume, as an example, that we are comparing two cartridges of identical case capacity (e.g., 6 CM and 6.5 CM). Practically speaking, bullet weight is greater in the larger caliber (e.g., 120 gr ELD-M versus 105 gr Horn BTHP, again assuming comparable SD and similar bullet design); muzzle pressure is similar but bullet muzzle velocity is less for the larger caliber; an identical case, heavier bullet, and greater chamber volume in a larger bore, means that to achieve identical muzzle pressures a comparable charge weight is used. So, approximating the above expression with relative relations, for the larger caliber:
less * (more + 1.75*same)
So, we can see that the relative recoil depends on exactly how much lower is the muzzle velocity, how does the powder charge compare, and how much greater is the bullet weight. In this practical example comparing 6 CM and 6.5 CM, we can use the following values (per Hodgdon data maximizing muzzle velocity for each while keeping peak pressure comparable),
6CM (105 BTHP, 43.7 gr SB6.5, 3156 fps at 60.2k psi peak): 3156 fps * (105 gr + 1.75*43.7 gr) = 549,461 gr*ft/s
6.5CM (120 ELD-M, 45.3 gr SB6.5, 3004 fps at 60.5k psi peak): 3004 fps * (120 gr + 1.75*45.3 gr) = 598,622 gr*ft/s
So, in this case the 6.5CM produces ~4.5% more recoil than does the 6CM. A different set of assumptions (not comparing similar bullet SD, identical case capacity, heavier bullet in the larger caliber, etc.) may produce a different outcome. If we assume maximal external ballistic performance of each caliber, and allow the other parameters that we previously held constant to vary, then
6CM (110 AT, 42.7 SB6.5, 3046 fps at 60k psi): 3046 fps * (110 gr + 1.75*42.7) = 562,672 gr*ft/s
6.5CM (150 MK, 42.6 gr H100V, 2713 fps at 60.3k psi): 2713 fps * (150 gr + 1.75*42.6) = 609,204 gr*ft/s
Now the 6.5CM has 8.3% more recoil, or about double the relative increase from before.