Custom Sizing
Through the styles you can specify the width and height of the card, and also the icon size through the main size option. Playing with icon size will growth the card unless a height is specified.
If you specify a width for the card, it has to be in px. All the cards without a width defined will use the remaining space on the line.

type: vertical-stack
cards:
- type: horizontal-stack
cards:
- type: 'custom:button-card'
entity: light.test_light
color: auto
name: s:default h:200px
styles:
card:
- height: 200px
- type: 'custom:button-card'
entity: light.test_light
color_type: card
color: auto
name: s:100% h:200px
size: 100%
styles:
card:
- height: 200px
- type: 'custom:button-card'
entity: light.test_light
color_type: card
color: auto
size: 10%
name: s:10% h:200px
styles:
card:
- height: 200px
- type: horizontal-stack
cards:
- type: 'custom:button-card'
entity: light.test_light
color: auto
name: 60px
styles:
card:
- height: 60px
- width: 60px
- type: 'custom:button-card'
entity: light.test_light
color_type: card
color: auto
name: 80px
styles:
card:
- height: 80px
- width: 30px
- type: 'custom:button-card'
entity: light.test_light
color_type: card
color: auto
name: 300px
styles:
card:
- height: 300px