Balquhidder is the modern spelling. It predates Henryson, but in between there have been many more conventionally phonetic variants, particularly in the 18th century. Balweder, Bowhether, Balwidder, etc.

The oldest one I know of is from a collection by John Hamilton, published in Edinburgh in 1796.
It's been posted in a related thread. Tannahill improved on it but didn't write it from scratch (and I doubt if Hamilton did either, the tune is decades older and presumably went with a song).