My son has a hoy balance bike..
According to the specs it has 12″ wheels, but the tyres say 12.5″

Is there really a 12.5″ tyre?

I was going to get some schwalbe black jack 12″, but looks like they may be half inch to small..
Are there any decent 12.5″ off road tyres?

I’d be suprised if they wern’t correct. Check the ETRTO on the tyre side and the Schwalbe website

Best upgrade available
[url=https://flic.kr/p/dzKdZ7]Tyre Upgrade[/url] by Tom Levell, on Flickr

What’s the ETRTO?

The tyres fitted are kenda 909a ETRTO 47-203, 12.5*1.75*2.25
reading online suggests that a 12 inch tyre will fit with the same ETRTO, Is that correct?

If the etrto numbers match then they will be fine
with cycle tyres be careful not to replace 1/2 or 1/4 with .5 and .25 as it not always the same
The ETRTO number helps get round this

A trip to sheldons web site will help