Presumably a weed?

Can anyone help identify this plant. Sorry the photos aren’t too good but it’s very small. At every leaf joint there seems to be a heart shaped bud(?) and it does seem to be spreading so I’m thinking, weed. Thought it might be Chickweed but not sure

 

I think I have lots of it too.
No idea what it is though - I've been pulling it up

 

Looks better than my lawn to be honest do I might let it run rampant

 

I'd leave it but then I'm not into green deserts.

 

Common knotgrass?

 

Looks like chickweed to me too.
Good food for budgies....and don't ask me how I know!