What do いんです and なんです do to the meaning of a sentence when tacked onto other words.
Examples:今日は佐藤さんの誕生日なんです。大きいけどとても軽いんです。(Are these just plain forms people use in every conversation and are just different from other words? Is this just to ease pronouncement of words? Or does it change the fundamental meaning of the sentance?

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it don't  change the fundamental  meaning.

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In the example you provide above, it's not いんです, but rather the い-type adjective  軽い + んです.
They both end in んです＝のです (の is contracted to ん), which can follow verbs and い-type adjectives as is, but need to add な if following a noun (誕生日) or a な-adjective (like きれい or 静か). The meaning of sentence final のだ/のです differs depending on the context, but one common use is to imply that what you are saying is an explanation for a previous context.

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from what i have learned,  it does not change the fundamental meaning, the format ん