A short shaft 25XD (back in the 80's) tipped the scales at 114 pounds.
The new 20 horse @ 115 pounds would be a good substitute (I don't like 4 strokes but this is a pretty sweet little motor - they also build the 15 horse now on the same platform).
The rating system from brake to shaft horsepower was not a "specific" date, but the major mfg's mostly changed over in the mid/late 70's so your 1980's boat would have most probably been rated for SHP (today's standard).
The actual weight of the motor is generally not the issue, it's the torque created where the motor is essentially trying to rip the transom off the boat.
The prop is trying to (crawl) under the boat which in turn "torques" (think crowbar) the top of the motor (powerhead) backwards. Since the bracket holds the motor it ends up creating thrust to move the boat forwards.
So if the loaded/rigged boat weighs say 1000 pounds, that is what is truly stressing the transom, not the 100 or even 150 pounds simply hangin' on the back - the 500 plus pounds of thrust (from a 20 horse) from the motor pushing on the transom to get the boat moving is easily 3 times the weight of even a heavy modern 4 stroke within your horse rating.
Don't get hung up on the weight of the motor. If the motor is significantly heavier than what it was designed for it will create issues, but not for the transom - it will change the attitude of the hull (make it bow high) which can lead to stability issues or proposing, but a couple hundred pounds on the transom won't "hurt" anything structurally...