1Describes something that is physically heavy — nearly the same meaning as 重い, but with a more casual, colloquial ring.
このスーツケース、思ったより重たいね。
This suitcase is heavier than I expected.
米を10キロも買ったから、袋がすごく重たい。
I bought 10 kilos of rice, so the bag is really heavy.
まぶたが重たくて、授業中に眠くなってしまった。
My eyelids felt heavy, and I got sleepy during class.
重たい荷物を持って階段を上るのはつらい。
Carrying heavy luggage up the stairs is rough.
2Describes a mood, atmosphere, or topic as heavy, oppressive, serious, or gloomy — an emotional or situational "heaviness" rather than physical weight.
リストラの発表があってから、社内の空気が重たくなった。
The atmosphere in the office became heavy after the layoff announcement.
彼女の話はいつも重たくて、聞いているこちらまで疲れてしまう。
Her stories are always so heavy that even listening tires me out.
重たい話題は避けて、もっと明るい話をしよう。
Let's avoid heavy topics and talk about something more cheerful.