How do I scale a PyGame image (Surface) with respect to its center?

Question

You missed to update the size of self.pixeltitlerect after the Surface has been scaled:

self.pixeltitle = pg.transform.scale(self.pixeltitle,(xsize,ysize))

# size of surface has been changed get the new rectangle
self.pixeltitlerect = self.pixeltitle.get_rect()

self.pixeltitlerect.center = (250,120)
self.screen.blit(self.pixeltitle,self.pixeltitlerect)

Or even shorter (see pygame.Surface.get_rect()):

self.pixeltitle = pg.transform.scale(self.pixeltitle,(xsize,ysize))
self.pixeltitlerect = self.pixeltitle.get_rect(center = (250,120))
self.screen.blit(self.pixeltitle,self.pixeltitlerect)

Do not scale the original Surface. If the original Surface is scaled it will get distorted. Keep the original image self.pixeltitleorig and scale the original image:

self.pixeltitle = pygame.transform.scale(self.pixeltitleorig,(xsize,ysize))

See also Transform scale and zoom surface

See the example:

import pygame
pygame.init()
window = pygame.display.set_mode((500, 500))
clock = pygame.time.Clock()

class ScalingSurface:
    def __init__(self):
        name = "pixeltitle.png"
        self.pixeltitleorig = pg.image.load(name)
        self.pixeltitle     = self.pixeltitleorig
        self.pixeltitlesize = self.pixeltitle.get_size()
        self.pixeltitlerect = self.pixeltitle.get_rect()
        self.pixeltitlerect.center = (250,120)
        self.mode="grow"
        self.grow = 0

    def update(self):
        if self.grow > 40:
            self.mode="shrink"
        if self.grow<1:
            self.mode="grow"
        self.grow += 1 if self.mode == 'grow' else -1

        xsize = self.pixeltitlesize[0] + round(self.grow)
        ysize = self.pixeltitlesize[1] + round(self.grow)
        self.pixeltitle = pygame.transform.scale(self.pixeltitleorig,(xsize,ysize))
        self.pixeltitlerect = self.pixeltitle.get_rect(center = (250,120))

    def draw(self, surf):
        surf.blit(self.pixeltitle,self.pixeltitlerect)

img = ScalingSurface()
run = True
while run:
    clock.tick(60)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

    window.fill(0)
    img.update()
    img.draw(window)
    pygame.display.flip()

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