Wee
Small, little - but also the universal Northern softener. 'A wee cup of tea' isn't necessarily a smaller cup of tea; it's a polite cup of tea. The word can shrink a noun, mark intimacy, soften a request, or do all three at once.
Etymology
From Middle English 'wey' / 'weygh', from Old English 'wǣġ' meaning weight - a small weight, hence a small amount, hence small generally. The journey from a literal weight to a generic diminutive happened across centuries; the modern adjective is documented in Scots from 1706 and has been in continuous use in Ulster Scots and Scots English ever since. The comparative 'weer' and superlative 'weest' are still in everyday use.
In a sentence
some says there was a wee girl from Tanderagee got herself killed. - Charles L. Graves, Humours of Irish Life, 1915
He was weer than me. - James Kelman, Kieron Smith Boy, 2008
Historical notes
Wee is the most distinctively Northern Irish word in everyday speech, and the one most likely to be the first marker a Northern voice gives a stranger. Its function as a politeness softener - rather than just a size modifier - is the key. A wee favour is a favour, not necessarily a small one; a wee bit of bother is bother, with the wee taking the edge off. The word works as a kind of social cushion that English without it has to do a longer way around.