What Weaker Side???
“Improve Your Weaker Side”
“Master Your Weaker Side”
“Dominate Your Weaker Side”.
Hmmm ... there seems to be some sort of problem with this thing called the weaker side. While I agree with the general concept that our non-dominant side is often less adept than our natural side, there are other factors to consider in this issue outside of equality.
Unequal Time
Humans rarely use both hands to the same degree. Drummers are obsessed with hand balance, yet we resort to dominant-handedness most of the time. So the other hand just hasn't had the same amount of practice, and so its development usually lags.
Equal Time
An exercise I did years ago had an interesting effect. I did everything with my left hand for a few weeks: getting dressed, shaving, eating, brushing my teeth ... anything that could be off-loaded. I don't know if this helped my playing, but it gave me an entirely new relationship with my non-dominant hand.
Form Follows Function
What does the 'other' hand (or foot) actually need to do? A drummer who plays mostly a back beat doesn't even need a hand to do it -- witness The Barbarian's 'Molty' or Rick Allen of Def Leppard. Typically the 'other' hand is doing the job we need it to do. It's only when we asked it to keep up with our 'good' hand that we struggle.
Genetics
We're all built and wired differently. Within our own bodies, things are wired differently from side to side. For example, some people take quite naturally to open-handed playing and some will never be able to do it because brain, nerves, muscles, etc. simply weren't laid down with that in mind. I resorted to traditional grip because matched grip in my 'weaker' hand persistently felt unnatural no matter what I did. So you do what you can.
It's good to work on developing our non-dominant limbs, but I think we need to give the so-called weaker side a break. For the most part it's doing a pretty decent job of what we need it to do. And if we want more, it's really comes down to focus and training.
(For more on Traditional Grip, see http://drumyoda.blogspot.ca/2013/04/why-traditional-grip.html)