In traditional Acol, the uncontested sequence 1♥-2♥ shows 6-9 points with three or four card support, whilst 1♥-3♥ is 10-11 points, at least four card support. The main reason for the wider ranging 2♥ bid is that opener has space for a game try.
A visit to your local club will reveal a lot of overbidders, who will raise the three level on a mere 8 or 9 points with four card support. That feels right because it preempts opponents out of the auction. But it is difficult for opener to guess what to do after 1♥-3♥ if the raise is 8-11 points.
We suggest the raise to 3 or 5 method. It works as follows (and similarly over 1♠):
1♥-2♥ = 4-7 count with four card support, or 6-8 count with three card support. (With a nine count and three card support, you would introduce a new suit.)
1♥-3♥ = 8-9 count with four card support.
1♥-2NT = 10-11 count, four card support, or enough for a raise to the five level (15+ points).
1♥-3NT = 12-14 count balanced, four card support.
1♥-3♠/4♣/♦ = splinter raises to game (singleton or void in bid suit): typically 11-14 count.
You can steal a point or two from the 3♥ and 2NT responses with a singleton.
Now what about continuations over the 2NT bid? One advantage of the method is that there is space for game tries. For example, consider 1♥-2NT-3♣-3♦. The 3♣ bid is a game try (long suit trial bid), over which the 3♦ bid is a return try.
If at any stage either hand wants to bid game they bid 3NT instead, to allow partner room to explore if he was always interested in slam. The first cue-bid at the 4-level shows a serious slam-try, and if it comes from responder, promises an initial raise to 5. For example, 1♥-2NT-3♣-3NT-4♦. Here 3♣ was initially just a game try, but would also be done on slam-going hands with clubs. Now 3NT was showing a raise to the three level accepting the game try, but giving room to opener should he have a slam try. Four diamonds duly showed the slam try.
1♥-2NT-3♣-4♣ is a raise to the five level, showing a club feature.
|Ax QJ10xxx Kxx xx
|Qxx Kxxx AJx Qxx
|Axx AJ10xx KJxx x
|Kx Kxxx Axxx xxx
|AK AQxxx KQxx xx
|xxx Kxxx Ax Axxx
|(4♠ instead of 4♦ is another possibility here.)
|Axx AJ10xx KJxx x
|xxx KQxx Axx AKx
|Axx AKJxx KQxx x
|KQx Qxxx Ax xxxx
|4♣ showed a singleton. Responder has the perfect hand, and marks time for one round in case there is a grand slam.
As with all conventions, you need to consider what you giving up in exchange. Here it is your natural 2NT response. Whether you have played this as 11-12 or 16+ points (Baron), you should normally be comfortable bidding a new suit instead, then 2NT, natural, next time.
2NT, natural, is still available in response to 1♣ or 1♦. One method to improve your minor suit bidding is to use inverted raises, but that is another story.