How can my flight change from half empty to full at check in ?
 

It depends on your carrier and of course on passengers. If you have to pay extra to get an allocated seat at booking or if you have to do an extra online check in process to allocate a seat for yourself, many passengers simply do not do it or very late. The flight most probably was not half booked, but many simply had not a seat allocated yet. Usually it is a bit cheaper to not get a fixed seat at booking, and of course most of us are cheapskates.

They probably only allocate seats to those who've paid extra, got some medical reason, are Gold Card holders etc. They know the rest of the seats will be filled but don't bother assigning numbers until people start physically arriving to check-in

Airline ?

Aircraft type ?

And there is always the possibility that they were carrying passengers from a cancelled flight, be it one of theirs or that of another operator.

Some carriers, at the computer allocates seats just before checkin starts. There are many variations.

It looks like you paid in advance for a choice of seat. Most people on that flight obviously didn't, instead they waited until check in and selected their seat for free or were allocated a seat when they checked in. It doesn't mean they didn't already have tickets well in advance, it just means they had not paid extra for a specific seat selection. For those who do not pre pay for a seat then the remaining seats are taken on a first come first serve basis at online check in.

Code share.

Hello turbidus and welcome to the cabin. That's a good point.

When anyone asks such a specific question, it really helps if you include the carrier and route - just as much information as you can.

When it is no longer practical or possible to book yourself a seat

At some point, once check in is available, I don't know when exactly that is, the flight will be under "airport control". My understanding of this is that all the seats are at the 'mercy' of the airline load control and are not available to the general public to select.

I've had my corporate travel agent ring me at the airport ton inform of a connecting flight delay saying they couldn't change the booking as the flight was under airport control. Fortunately, the airline had already through checked me and given me the boarding pass so it was their responsibility if I missed the connection.