Yes, they double, then a few techs researched later they double again.  The red or weapon and invasion techs are the worst for this.  I researched this by using the search feature in Gal Civ forums (upper right corner of your screen) and found numerous threads but nothing was specific enough to really use as a guide to prevent or delay this from happening.  This tech inflation isn't a gradual type of phenomena it's one turn your fine then the next the red or other techs have doubled (the other techs take a bit longer to be affected).  I have tested this in a couple of games and through trial and error I can only make the simplest of assumptions as to how it works.  I have read that the larger galaxies (say gigantic and immense) have this happen the most.  Perhaps you play in smaller galaxies and don't see it. 

I am aware of the increase in tech costs within a branch of the tree, but what I am talking about is a doubling of this base amount.  I have documented all of the base tech costs for my races tree and I am currently in two games that have the tech costs doubled (in one) and quadrupled in the other.  Check out the other threads (use the search function in the upper right corner, for criteria use 'tech cost increase') as this is a common experience in at least ToA if not the other expansions.  I have played mostly the original Gal Civ and I didn't notice this at all.  With the expansions this is apparently not the case though.

There is a base multiplication for galaxy size and research rate from the start (see the wiki entry for galaxy settings).  Inflation is on top of that and yes, the more techs you research the more inflation goes up.  However it is not readily apparent until you get 40-50 techs in.  The amount of inflation was curtailed in 1.92 (I think, see here).  Double the cost sounds about right.

You have to build more research facilities, economic starbases, and mine research resources to overcome the effect.  Red techs get more inflation than others, which somewhat penalises an exclusive focus on military technology.

IDK, in the two games that I started monitoring tech costs the doubling, of weapon/invasion, techs starts at around 16 techs researched and the non military techs about 26 in.  As long as it affects the other races I can handle it okay.  If not, then I will have to rethink my obscene/suicidal Gigantic games. 

It appears that the other races are affected.  I finally got through my latest marathon game (10 game years).  I will play a couple or three more on obscene then go for suicidal.  Thanks for the info! Peace