Everything should actually be and feel lighter on spinning tackle than casting rods and reels, but closer nowadays. If they feel the same to you, your spinning tackle is either too heavy, or your casting rod and reel is too light.
And, the balance point on the spinning reel should be right at the hand holding the rod, and if you have used spinning gear a lot as it appears you have, that likely gives it an advantage over the casting gear.
Even when you get out on the water, the spinning reel retrieve is "rod based" where the line is pulled in with the rod then reeled up with little or no reel resistance; with a baitcaster, the reel acts, at times, as a winch.
Throwing crankbaits all day long has to require much more effort than a lightly casted drop shot or a weightless worm.