Place with high humidity prefer faster shuttle, while place with dry weather normally prefer slow shuttle. High humidity means higher air density due to higher water vapor content, and these contribute to more resistance to shuttle flight.

In halls with low ventilation and hot afternoon (especially after short shower), sometimes 77 may feel too slow, hence some place they play with 78.

It does not affect the racket tension, it is the humidity that affect the shuttle, hence the feedback and feel.

If not mistaken, the correct way to measure shuttle speed is to do a standard high serve. It should land within the range of few inch around baseline.

If you can't serve that high or that far, you can still tell by simply perform a high serve and almost immediately, you can tell if the shuttle is too fast or too slow compare to your normal play.