Practice playing third intervals smoothly
Phrases with a series of thirds are very common, but to play them lightly and legato requires a special technique. Here’s the idea. After playing the first third (say right hand C and E, played together with 1 and 3 fingerings), then hold E while you raise the other finger from C; then play D and F together. Watch the video to see how it done.
Just play lightly and everything is going to be OK! Series
You can practice more with this technique:
Hanon No.15 and Czerny No. 9 and 10 Play Along
Hanon
complete score --- https://imslp.org/wiki/The_Virtuoso_Pianist_(Hanon,_Charles-Louis)
This is good website, too --- https://www.hanon-online.com
Czerny
complete score --- https://pianoexercises.org/exercises/czerny/)
specially I uses "125 Exercises in Passage Playing"
Schubert 18 Viennese Ladies' Ländler D.734, Op.67