What is relationship between molecular weight distribution of PE and its strength?
I have found an old paper that might answer your question, which is:

"The Effect of Molecular Weight Distribution on Polyethylene Film Properties"
P. J. Perrono, P. B. Lederman, Polymer Egineering and Science, 1972, 12, 5, 340-345 (DOI: 10.1002/pen.760120505).

The properties of polyethylene evaluated in this paper as a function of the molecular weight include film gloss, haze, tear resistance and film impact strength.
This study shows that broadening the molecular weight distribution increases haze and reduces film gloss. Further, it was shown that a linear relationship exists between film gloss and external haze. Both values are measures of surface irregularities in the film which are affected by the drawing characteristics of the polymer. A broader molecular weight distribution results in increased impact strength as measured by the Dart Drop Impact Test. This is, it is believed, a result of the increase in long chain branching of the higher molecular weight fractions of the polymer which cause a higher degree of molecular weight entanglement at the branch sites. In contrast the tear strength is reduced as the molecular weight distribution broadens because of the low molecular weight fraction in the broad spectrum material which tend to decrease resistance to tear.

Hope this helps.