Responder’s double of an opponent’s suit overcall, to whatever level, is for take-out, and known as a negative double. It usually shows:
• Four card or longer support for the unbid major suit: support for an unbid minor suit, unless responder has something else to bid if opener bids the minor suit eg 1♣ (1♠) X shows either hearts and diamonds, or maybe one of these, 6+ pts.
The higher you’re forced to bid, the stronger the hand must be. A good rule is that you need to be a King (ie 3 pts) better for each level higher. Eg 1♣ (2♠) X requires at least 9 pts, as it forces to the 3 –level, and 1♣ (3♠)X requires 12+, as it forces to 3NT or the 4 level.
• With a five+-card suit, responder bids the suit rather than doubling, showing 10+ points. This is forcing. (1♣ (1♠) 2♦/♥). If responder doesn’t have enough strength to introduce the suit at the required level, responder starts with a negative double, planning to bid the suit at the next opportunity, eg 1♣ (1♠) X P 2♦ P 2♥ would show a weak hand (fewer than 10 pts), and 6 hearts.
• Opener makes an appropriate bid after hearing a negative double by responder, based on what is in THEIR hand, and also who strong they are, ie minimum (13 – 15), medium (16 – 18), or maximum (19 – 20).