We have this little guy living in our bathroom. She's our pet.
I absolutely HATE spiders... BUT... there were these five little teeny tiny baby spiders in our bathroom and I vacuumed them up and killed them all... except one.
And I didn't have the heart to kill her, so I left her there. She was about 3mm in size... she's now about 1/4 inch in size, including her legs... and she's been there about 7 months or so.... lol.
She never leaves that one corner. She's got about a 6 square inch part of the bathroom that she inhabits and we leave her alone...
So no... little spiders do not always grow up into big spiders