It is simply the case that New Hampshire started out with very high representation and expanded membership in the House of Representatives through the 19th and early 20th centuries.

According to the NH house of representatives website, the first session of NH house in 1776 started out with 87 members "each one representing 100 families". In the book New Hampshire 1776 census by Jay Mack Holbrook, he provides an estimate of 83,500 for the state population in 1776.

The NH house website goes on to say:

As time passed and the population increased, the number of Representatives grew, until there were 443. In 1942, a constitutional amendment limited the size of the House to 400 but not less than 375 members.

Again looking at census figures, the 1940 census population of NH was 491,524 and we know there were 443 representatives.

With some quick arithmetic, we can calculate the following:

in 1776- 83,500 pop/ 87 reps = 959.8 persons per rep.

in 1940- 491,524 pop / 443 reps = 1,109.5 persons per rep.

I think it is reasonable then to presume that New Hampshire tried to maintain a ratio of representation of approximately 1000 constituents per representative up until 1942, when further expansion of the legislature was felt to be unwieldy and number of reps was capped permanently at 400.

If we also look at tables of population represented by State Legislators we can also notice some interesting patterns. New Hampshire has the largest state house of all, but Massachusetts with 160, Maine with 151, Connecticut with 151 and Vermont with 150 are all in the top 10 for largest legislatures. Rhode Island with 75 is the only New England state with below-average number of state reps.

If we sort the table by "population per representative", New Hampshire has the smallest population per rep with 3400, Vermont 2nd place with 1:4200, Maine in 4th with 1:9000, Rhode Island 8th with 1:14,000, Connecticut in 12th place with 1:24,000 and Massachusetts in 25th place with 1:44,000 (but still below the national average of 1 state rep per 61,000 persons).

What all those ratios amount to is: I think there is a cultural attitude in New England to strive towards high levels of representation per-capita. Yes, there is a general trend where smaller states tend to have fewer constituents per representative, and four of the six New England states are very small with populations under 2 million.

But, given that Connecticut (pop 3.6 million) has a much better representation ratio of 1:23,000 than peer-population states Utah (3.3 million, 1:43,000) and Oklahoma (3.9 million, 1:39,000). And Massachusetts (7 million, 1:43,000) does better than Indiana (6.7 million, 1:68,000) Tennessee (6.9 million, 1:70,000) and Arizona (7.1 million, 1:119,000). I think it is supportable to say that New England states do try harder than average to have more representation and smaller constituencies.

If there truly is a New England ethos around keeping constituencies per representative as small as feasible, then New Hampshire and Vermont seem to be the most fervent states in expanding their legislatures to maintain these favorable ratios.