AFAIK, the size of an enum is the smallest integer needed to hold the number of cases. So if you have less than 256 cases, it'll only need one byte. If you have between 256 and 65536 cases, it'll occupy 2 bytes:
enum E {
case a0, b0, c0, d0, e0, f0, g0, h0, i0, j0, k0, l0, m0, n0, o0, p0, q0, r0, s0, t0, u0, v0, w0, x0, y0, z0
case a1, b1, c1, d1, e1, f1, g1, h1, i1, j1, k1, l1, m1, n1, o1, p1, q1, r1, s1, t1, u1, v1, w1, x1, y1, z1
case a2, b2, c2, d2, e2, f2, g2, h2, i2, j2, k2, l2, m2, n2, o2, p2, q2, r2, s2, t2, u2, v2, w2, x2, y2, z2
case a3, b3, c3, d3, e3, f3, g3, h3, i3, j3, k3, l3, m3, n3, o3, p3, q3, r3, s3, t3, u3, v3, w3, x3, y3, z3
case a4, b4, c4, d4, e4, f4, g4, h4, i4, j4, k4, l4, m4, n4, o4, p4, q4, r4, s4, t4, u4, v4, w4, x4, y4, z4
case a5, b5, c5, d5, e5, f5, g5, h5, i5, j5, k5, l5, m5, n5, o5, p5, q5, r5, s5, t5, u5, v5, w5, x5, y5, z5
case a6, b6, c6, d6, e6, f6, g6, h6, i6, j6, k6, l6, m6, n6, o6, p6, q6, r6, s6, t6, u6, v6, w6, x6, y6, z6
case a7, b7, c7, d7, e7, f7, g7, h7, i7, j7, k7, l7, m7, n7, o7, p7, q7, r7, s7, t7, u7, v7, w7, x7, y7, z7
case a8, b8, c8, d8, e8, f8, g8, h8, i8, j8, k8, l8, m8, n8, o8, p8, q8, r8, s8, t8, u8, v8, w8, x8, y8, z8
case a9, b9, c9, d9, e9, f9, g9, h9, i9, j9, k9, l9, m9, n9, o9, p9, q9, r9, s9, t9, u9, v9, w9, x9, y9, z9
}
MemoryLayout<E>.size // $R0: Int = 2
If you have more than 65536 cases, then... step away from the computer.