I was hesitant to answer the question but decided to go ahead and jump in. JWs are worried that it might show their faith to be weak if they go to doctors, along with every other denomination of believers. The fact is, our faith is weak nearly all the time these days.
We want to show how strong we are but we end up getting worse off because of the pride we have in our (weak) faith. We are not supposed to be prideful of anything. Pride is what caused Satan to be cast out of heaven and it will cause us to stumble and fall.
When Jesus healed anyone in the Holy Bible, He would say, "Your faith has made you whole. Go and sin no more"
In finalizing, we are weak in the faith because we have so much to depend upon rather than God. We seek to fulfill our own desires instead of looking to God for our needs. A child should not be forced to live without either or both parents.