They call their music “The Woodstock Sound” and they don’t mean the festival. The players who comprise The Weight Band—their name is a giveaway— have deep ties to the music most closely associated with the Upstate New York burg and its most famous musical spawn. Particularly, guitarist/mandolinist Jim Weider, a native of the town, spent years playing guitar for the post-Robbie Robertson incarnation of The Band and remained a musical partner of Levon Helm’s until the latter’s death in 2012. The album, their debut, is in fact dedicated to Helm, Rick Danko and Richard Manuel. But that’s not to imply that The Weight Band is a full-on tribute project. Although the arrangements share blatant similarities to the style of their chief inspiration—“Remedy,” the live bonus track, would not have been out of place on Stage Fright or on the stage of The Last Waltz —the quintet (which also features keyboardist/horn man Marty Grebb, keyboardist Brian Mitchell, bassist Albert Rogers and drummer Michael Bram) has fashioned its own take on the music, which they first performed in Helm’s barn five years ago. Two tracks, “Common Man” and “You’re Never Too Old to Rock ’n’ Roll,” credit Helm as a co-writer, and “Day of the Locusts” was originally tucked away on Dylan’s 1970 New Morning set. But “I Wish You Were Here Tonight” and “Heat of the Moment” detour just far enough away from the source to convince a listener that The Weight Band has the goods to expand in other directions, and their spirited workout on Garcia-Hunter’s “Deal,” sung by guest Jackie Greene (who also contributes snazzy slide guitar), is a swampy beast that finds its own way even while managing to honor both the Dead and The Band.