I leaned violin in strings class in school. The students were asked to perform for the parents at the year-end concerts. I find that I have more confidence playing in front of the audience when my pieces were memorized. My eyes often skipped over bars or lines.
When I started piano. I wasn’t proficient reading 2 staffs at a time. Ended up learning pieces in small chunks and memorize them. I still lean towards memorizing than reading my pieces.
Whether a piece is easy or hard to memorize depends on how the LH & RH parts are arranged. If the parts are straightforward with lots of repetition, it’s easy to memorize. One of the pieces I learned a year ago is an arrangement is Simon & Garfunkel “Sound of Silence” with 5 verses. There are slight variations between verses but still repetitive so very little effort to play from memory. The last piece I worked on was the Bourree from Bach Lute Suite 1. Besides some awkward fingerings, got the piece more or less memorized after a week.
If a piece has scale runs or straightforward chord changes, it’s easy to memorize. If you see a scale run, you just need to know the start & end notes than reading the sequence 1 note at a time.
You can get into the habit of learning in small chunks. After every few bars turn the page over and try to recall the notes as much as possible. Going to get easier after a while.