Say there is a 3/8 oz to 1-1/4 oz lure weight on a rod. Would there be less sensitivity in a 3/8 oz jig compared to say a 1/2oz jig?

No. What would change is the rate of fall, with the 1/2 oz falling a bit faster everything else being equal. Extra weight makes the jig a little easier to keep track of in windy conditions, and might give you better feel for a bite...

No, I believe more sensitivity is transmitted thru the line than the rod.

Guys have it right.

As long as you stay within the paramaraters with your bait and sinker weight you should not have any problems feeling bites or setting the hook.

The lure weight ratings on a rod refer to the weight required to load the rod properly for efficient casting. Exceeding the rating by a large degree on either end can make keeping contact with the bait difficult but doesn't affect sensitivity as it is normally traditionally thought of in term of detecting bites.

Imagine you've tied on a 1/8oz jig on that rod, and tried to cast it. The rod would not load (flex) with a lure weight that low. It would be like casting with a broomstick.

Now, tie on a 3oz swimbait. The rod would load very deeply into the blank. It would flex during the cast much farther than would be efficient. Do this, and put too much effort into the cast and your rod could snap.

Would there be less sensitivity in a 3/8 oz jig compared to say a 1/2oz jig?

Well that weight difference isnt much to be able to notice but with say a SK Bitsy Bug 1/8oz/craw to 1/2oz/craw football jig the reading of the bottom will be transmitted better by the 1/2oz jig. The lighter jig set-up will not contact a rock, stick, pebble, any transition as hard as the heavier jig. Lighter might float over giving less feedback fall slower like K_Mac mentioned meaing when it does contact its not contacting as hard so not as much feedback sent to rod. Ive fished both set-ups on the same rod and notice a difference. To take to extreme a feather falling on your arm you might not notice but a penny falling on your arm you will/should.

Sensitivity has nothing to do with with weight ratings on a rod.

alright thanks guys i was just currious

Pretty much what quake is saying. Tie a feather to a string, close your eyes, let it fall. Will you be able to tell as easy when it hits the ground as lets say a rock? Of course not. I know this is an extreme example but there is a probably is a slight difference in what you are feeling on the bottom. Most likely 1/8 of an ounce won't make a noticable difference though.