a simplified explanation is that:
non-weighted (or true) reels: the odds of any symbols landing on a particular line are absolutely EQUAL. the machine's payout is determined by the number and way the symbols are layed down on each reel strip. if a reel strip has 3 blanks, two cherries, and one jackpot symbol... ALL 6 symbols have equal probability of landing in a particular spot, but since there are more blanks, you'll see them more. if YOU made a slot at home out of toilet paper rolls and drew in symbols, then spun the rolls.... this would be a simple non-weighted slot.
weighted reels: not as above
take the toilet paper roll slot you just made and add little weights to the blank symbols....
essentially, weighted reels were created for the 3 reel slots like double diamond or red,white, and blue because there wasn't enough space on the reels. so instead of the rng result being 1=blank, 2=cherry etc, now it became 1 or 2 or 3= blank, 4 and 5 =cherry, etc. (the physical reels became worthless and just for visual representation)
video slots are SUPPOSED to be non-weighted since they don't have the physical and mechanical limitations of regular slots. ie, with video slots you can have reels with hundreds of symbols if you want.
why a video slot would have weighted reels is probably best left for another thread and more knowledgeable members. this is a simplified explanation until one of the senior members jump on.