Is Morgoth, the original enemy in J. R. R. Tolkien's Middle-earth ever visually described? I envisage him as a bigger, meaner version of the physical Sauron, but I cannot find any reference in The Simarillion.
Depends. He takes on various forms at different times. He's mostly described as a huge dark man and this is the form he takes and is locked into after his first imprisonment.
His first appearance during the creation and the First War was
"a mountain that wades in the sea and has its head above the clouds and is clad in ice and crowned with smoke and fire; and the light of the eyes of Melkor was like a flame that withers with heat and pierces with a deadly cold."
He lost his foot and suffered various un-healable wounds after his combat with Fingolfin and burnt his hands stealing and holding the silmarils.
Melkor was grandiose. His helmet, as the Morgoth, was so heavy Beren could not lift it [Lays of Belereiand, 8.4136-4137], and he had a scar and limp [12.3604-09, 3615-3617, 3632-3634]. Melkor's physical form in the beginning is described as:
because of his mood and the malice that burned in him that form was dark and terrible. And he descended upon Arda in power and majesty greater than any other of the Valar, as a mountain that wades in the sea and has it head above the clouds and is clad in ice and crowned with smoke and fire; and the light of the eyes of Melkor was like a flame that withers with heat and pierces with deadly cold. [Silmarillion; Ainulindalë]
He is also said to have walked around in various "shapes of power and fear" [Of the Beginning of Days]
he put on again the form that he had worn as the tyrant of Utumno: a dark Lord, tall and terrible. In that form he remained ever after. [Of the Darkening of Valinor]
Don't over-estimate how big Melkor, or any of the Ainu were. There is also another description of him when he battles Fingolfin:
Morgoth came, climbing slowly from his subterranean throne, and the rumour of his feet was like thunder underground. And he issued forth clad in black armour; and he stood before the King like a tower, iron-crowned, and his vast shield, sable unblazoned, cast a shadow over him like a stormcloud...
Melkor held aloft Grond, the Hammer of the Underworld, and swung it down like a bolt of thunder... Grond rent a mighty pit in the earth, whence smoke and fire darted...
Morgoth bore his shield upon him. Thrice he was crushed to his knees... Morgoth set his left foot upon his neck, and the weight of it was like a fallen hill. Yet with his last and desperate stroke Fingolfin hewed the foot with Ringil [The Ruin of Beleriand]
Morgoth is big but not like a giant. When he put his foot on Fingolfin's neck he could still use his arm to swing his sword.