HOW LONG DOES IT TAKE TO STRENGTHEN WEAK MUSCLES?
A recent study (ncbi.nlm.nih.gov/pubmed/26981714) found that a short term activation training program (of just six days) was effective in improving glute med activation through improved motor control and less inhibition of the muscle. So if the muscle you want to strengthen is just inhibited and not wasted / truly weak, changes can happen very quickly. To get these improvements you need to ensure:
1) Your starting position is right
2) Your understanding of the muscle is accurate
3) You receive the right cues to activate the muscle
4) You reinforce it with lots of repetition
On average exercise should be progressed slowly with regards to intensity but done 3 x a day. Protein synthesis will occur 2-4 hours after exercise and will immediately start building muscle.