C64 Assembly Rendering a Sprite

As @Jester pointed out in the comments, the X-position and Y-position memory addresses are wrong. The correct addresses are $d000 and $d001:

; set x and y position
lda #$80
sta $d000
sta $d001

This is the corrected code:

    .segment "CODE"

    ; set sprite pointer index
    ; this, multiplied by $40, is the address
    ; in this case, the address is $2000
    ; $80 * $40 = $2000
    lda #$80
    sta $07f8

    ; enable sprite 0
    lda #$01
    sta $d015

    ; set x and y position
    lda #$80
    sta $d000
    sta $d001

loop:
    jmp loop

    .segment "GFXDATA"

    .byte $FF,$FF,$FF,$FF,$FF,$FF,$FF,$FF
    .byte $FF,$FF,$FF,$FF,$FF,$FF,$FF,$FF
    .byte $FF,$FF,$FF,$FF,$FF,$FF,$FF,$FF
    .byte $FF,$FF,$FF,$FF,$FF,$FF,$FF,$FF
    .byte $FF,$FF,$FF,$FF,$FF,$FF,$FF,$FF
    .byte $FF,$FF,$FF,$FF,$FF,$FF,$FF,$FF
    .byte $FF,$FF,$FF,$FF,$FF,$FF,$FF,$FF
    .byte $FF,$FF,$FF,$FF,$FF,$FF,$FF,$FF

And here's a picture of it in action:

You can use VIC_SPR0_X and VIC_SPR0_Y if you include c64.inc. This can make your life much easier.