strength increases the amount of damage that is possible for an attack, attack actually inreases the power.

If you think of it as a bottle of water and water is the amount of damage.
with base strength and base attack you have a 0.5 l bottle of water and the bottle is full to the brim. so you do consistant alright damage.

If you increase str by alot and dont increase attack, you now have a 1 l bottle of water but you still only have 0.5 l of water in it so the attack damage is still the same.

If you increase str and attack but not as much as you tried putting everything into str, you will have a 0.75 l bottle of water and it full the the brim meaning your attack power has increased consistantly.

hope my dodgy analogy helps