Fighting as an individual hoplites would probably fight with the doru underhand but I can't see how it would be done in a phalanx. They charged in that formation and there are even instances that they lined up 16 deep. Phalanx against Phalanx was a pushing competition with stabbing in between.
Given that it was common to have a a pike as a counterweight on the end of the doru and also to use if the spearhead broke it would probably impale the man behind during a charge.
For a man that trains it, holding a spear overhand for extended period of time should not pose much of a problem.
One of the training excercies I was made to do regularly in the army was holding a H&K G-3 over my head by the front of the barrel, at first most guys could maybe hold it in under a minute, but after 6 month most could hold it three of four times that or longer, and that is without any balance. The G-3 weighs around 10 lbs, or 4.5 kg.
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