You should not have a lot of weight on your hands; that indicates a poor fit on the bike. Too much weight forward but pressure on hands, shoulders, neck.

Ideally, you should be able to put have your hands on the flat part of the bar then be able to remove them without falling forward. If you are correctly fitted on the bike but can't do this, build up your core muscles.

You probably aren't correctly fitted to the bike and will need to shift weight back by moving the saddle and/or raising the bars and/or shortening the stem.