I think Thanos has respect for almost anyone in his fight. He is unique for a villain, in which he has an enormous level of empathy... which makes him specially relatable.

^Yeah, it's just because Tony proved himself a formidable foe in battle.

Because Tony was a genius and he also was able to make Thanos bleed a little bit.

I think Thanos respects a good fight and Tony was that for sure. Also, Thanos didn’t appreciate Loki’s betrayal, which is the opposite to how Tony’s challenge him. No one likes to be betrayed, but for Thanos he seems to respect the human who tries to find a way to equal strengths with him to draw that drop of blood over the Asgardians who attempts to lie and deceive him so he can stab him. Thanos doesn’t care for either guy because they want to stop him for his goal, but his response to Tony is very different from Loki, which is due to how they challenge Thanos.

Thanos also knew of Tony before Infinity War, though. I always thought that Thanos heard about the nuke and the wormhole and gained respect for Stark because of that, and that respect only increased when he managed to draw blood like what the others said.

All good thoughts thank you

I think he respects Tony because Tony risked his life flying a nuclear missile into a wormhole, destroying Thanos' Chitauri ship and killing most of his Chitauri army. Thanos is impressed by people like that ("The strongest choices require the hardest wills" or whatever the exact quote was.)

If Thanos hasn’t the time stone he could see the future possibilities and know that tony is very dangerous to his operation in endgame, but this is just a theory.