CAMBRIDGE — Rivers Cuomo could not contain his glee Sunday night at the Sinclair and his good cheer was contagious.  The Weezer singer-songwriter-guitarist repeatedly thanked the sold-out crowd for coming out to celebrate the band’s superb new album, “Everything Will Be Alright in the End,” which recently debuted at No. 5 on the Billboard albums chart, and gushed at one point “I love this! It’s so much fun!”  And it was, an intimate treat of a first look to precede a tour at much larger venues no doubt.  The quartet — augmented by a versatile, but unintroduced, utility man on keys, guitar, and backing vocals — played a jubilant, jam-packed 90 minutes that included a nine-song acoustic opening set of Weezer oldies, the entire new album, and a quick encore.  The show began with Cuomo taking the stage solo for a winsome “You Gave Your Love to Me Softly.” Each member of the quartet joined in turn as the songs progressed. Guitarist Brian Bell emerged for warped warbler “Why Bother?” Bassist Scott Shriner — sporting a serious cast on his right arm and part of his hand that miraculously didn’t impede his playing a bit — materialized for his lead vocal turn on the intense “King.” And finally drummer Pat Wilson popped up to lay down the beat for “El Scorcho,” one of many tunes to be heartily cheered and sung by the crowd.  Cuomo responded to cheers of “Welcome back!” with gratitude and explained that many of the songs from angst-ridden, fan-favorite album “Pinkerton” were written during his time in Cambridge while attending Harvard, shouting out his old dorm and even giving the street address of one apartment. With perfect timing Bell chirped, “So thanks for making him feel like such an outsider, this song is called ‘The Good Life.’ ”  Whether playing acoustic or bringing the brawn of “EWBAITE” — an appealing and tuneful collision of new wave, power pop, ’80s hair metal, and even a bit of prog-rock pomp or, in other words, classic Weezer — the band was clearly having a good time with each other, the crowd, and the celebratory atmosphere.  (That atmosphere would’ve been enhanced greatly if the house lights had been turned off during the acoustic set, a curious choice that made the stuffed room stuffier.)  The electric set tackling the new album — bolstered by video screens scrolling through the lyrics — included sing-along single “Back to the Shack,” a robed fan choir on “Foolish Father,” and the beguiling “The British Are Coming,” which moved from a pastoral lilt into full-tilt rocker.  The regular set ended with the epic, guitar fury trilogy of “The Wasteland,” “Anonymous,” and “Return to Ithaka.”
Weezer celebrated the release of its new album with a jubliant, and intimate, show at the Sinclair in Cambridge Sunday.