One picture can carry all four uses: a gap that has been squeezed out of existence. A hand closes on a rail until no space is left between skin and metal. That is the starting image, and every other use is the same picture with something else standing in for the hand. Rules can close around what people may do. Houses can close on each other along a lane until there is no air between them. A face can close on a feeling until only a small stiff smile gets out. In each case the question is the same: how much loose space is left? Tightly is the answer none.
From the word’s history
The packet's Wiktionary entry gives the make-up of the word as tight + -ly. So the adverb is simply the adjective tight plus the ending that turns it into a way of doing something: in a tight manner. The comparative and superlative usually appear as more tightly and most tightly; the one-word forms tightlier and tightliest are recorded but rare.
封包裡的 Wiktionary 說明這個字的組成就是 tight（緊的）加上 -ly。-ly 把形容詞變成「用某種方式」，所以 tightly 字面上是「用很緊的方式做」。比較級一般寫 more tightly、most tightly；資料裡也收了 tightlier、tightliest，但很少見。
packet evidence: Wiktionary entry for tightly, source_ref kaikki:3f6f69a190036ae4:1014758993 ("From tight + -ly.")
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