You need a #00 Phillips for most screws on your Macbook (maybe a #0 will fit better there, not sure anymore)
I keep several different phillips size bits, and just use whatever is a better fit.
I have a long bitholder (10 or 12-inch) for magnetic screwdriver bits that gives good torque (and good control) which I need occasionally for some of those stubborn screws.
Make your best choice to have a phillips size that is a snug fit in the screw head, which will give you the best results, I think.
Watch out for worn bits, as those can cause you grief, if you strip out some of those small screws. I replace the smallest bits about once or twice a year.
With THAT in mind, try a _new_ screwdriver, with correct size tip.