These agreements are supposed to reduce barriers in both directions, so there is an interest for businesses on both sides to reduce friction and allow greater access to foreign markets.

Unfortunately, this laudable process has been more and more hijacked by special interest groups, to the point where international treaties are used as backdoors to impose legislation that would otherwise be very unpopular at home. An MP voting in, say, New Zealand to extend copyright terms, would get a lot of stick; but now he can say "hey, there is some good with the bad, less barriers are good for the economy blablabla" and vote for the whole bundle with significant political cover; he can then collect his copyright-lobby cheque AND keep his seat, win-win.

In a way, this is natural; this sort of dealmaking was commonplace at local and national level at most times in history, and it took a lot of effort to make it fairly transparent through the democratic process; now it gets done at a global level, where there isn't a democratic process yet -- we don't vote for a "world parliament" where this sort of issues could be thrashed out in public, we rely on ambassadors and special envoys with wide negotiating powers and no accountability, which naturally results in corruption.

Well ... those kind of agreements are used often as vehicles to bypass national sovereignty. Lets say that official X wants to make law Y, that has a slim chance of passing trough the national legislative body or public. But if it signs an agreement that have these provisions, than the country has to change its laws to fulfill the treaty.

Due to reasons US Congress can vote only binary on approving the agreement. Take it as is or throw it all away. In other places it is similar. So there are internal politics to consider.

The carrot is that companies pay the politicians. The stick is that the companies stop paying the politicians.

I imagine the multinationals get to play both sides of the negotiation — they can lobby it to both governments. Hence it's probably mostly all carrot ("Sign and you'll get lower barriers to your own products"). I can imagine there may be some stick too: Sign this or you'll lose access to Disney and pharmaceuticals.