it does and for every extra level maxed research center you get 10 extra points to make research speed faster
example: 2 days can turn into 12 hours by having more research centers(maxed of course).
Also, a colony's governour enhances that colony's research speed through the financier skill.
For example, if a colony has research facility lvl 10 and a governour with, say, 50 financier points:
that means that this colony's research speed is 10 + 50% = 15
All the speeds from all your colonies are then summed up to form your actual research speed which you can see in the research panel.
Raise your colonies governours on financier properly, and you can increase this speed greatly.
It's how I managed to get a research speed of nearly 200! (and rising still!)
I checked my speed just now, summing up all my colonies together with what I would get from research facilities and financier skill alone, and the result was exactly the same as the research speed I see in my research panel.
So in my case, the weapon, engineering and high energy facilities don't provide any research speed bonus whatsoever...
Are you sure that increase wasn't because of a governour's financier skill increase?