A different yarn weight would definitely affect the gauge. Some of it depends on your knitting style--loose or tight. You'd have to do a swatch and then some math to see how to adjust the pattern. You may have to knit 2 inches longer or shorter than the pattern, or less or more repeats. It would also change the texture, if the yarn is too thin, it would be gauzier, if it is too thick for the needle, it may not produce a fluid fabric and might also be hard to knit. The wrong gauge can give you a too thick, short, tight sweater that doesn't move well. Sometimes these are design choices. If you are a beginner, I would advise you to go with the suggested yarn weight until you know your knitting tendencies. Hope this helps.

I would not suggest you use a weight that is too different than the suggested weight but sometimes a different brand may be the same weight but have a slightly different gauge. Worsted weight for instance can have anywhere from 18 to 23 stitches in 4 inches and they are interchangeable but you wouldn't want to use a bulky yarn or a fine yarn because the garment would not come out right.

In any case you should always do a swatch before you start your garment even if you are using the needles and yarn suggested so you can be sure your garment will turn out right. Using the needles called for cast on half the number of stitches called for in the yarn gauge on your yarn label. Do half the number of rows called for and then measure the length and width. If your label says 18 stitched and 24 rows measure 4 inches on a 4.5 needle you should have a 2 inch square. If you don't then up or reduce the needle size--usually by the next size needle

You can use any yarn you choose....but your gauge must be the same or your garment won't be the right size!! You can knit a sweater that calls for worsted yarn and knit with sock yarn....but you will have to make sure your gauge is the same.