Varmint barrels up to 24" are used all the time without any issues as are space guns but there is an added risk of the upper cracking if the rifle is dropped. From the weight alone it would not be a problem. Consider national match 20" barrels, a sleeve and additional weight is added, my competition rifle has 3 lbs of extra weight under the handguards while this weigt bears on the threaded outer area of the upper rather then the inside hole the barrel slipps into, it still adds weight to the upper.
The reletively few 24" heavy barrel uppers that have sustained cracks when dropped are in my opinion due to the added weight and length working together to "lever" the upper when the rifle was dropped. I do not think you have anything to worry about with a 16" varmint barrel.