I wouldn't characterize their infantry formations as weaker necessarily, but Russia has often had a manpower advantage over its rivals that it has used to its advantage. Russia has been involved in many wars and battles in its history, I'm just going to focus on the major wars of the Russian Empire in my answer.

This goes back to at least Peter the Great in the Great Northern War in the early 18th Century that was primarily against Charles XII and the Swedes. In that war Sweden generally did have better quality formations, but Sweden was at the very top in Europe in terms of military effectiveness at that time. They would have compared well to any other European army in terms of training, tactics, and weaponry. And Charles XII was one of the leading tacticians of his generation. I think it's fair to say that Russia did rely on an attrition strategy to lure Charles XII in and wear him down by dint of numbers over many years of fighting, both at the strategic and tactical level.

Fast forward to the Napoleonic Wars and one of Russia's main strengths was once again the ability to raise large numbers of men. That being said, Russia did not have a huge numerical advantage when Napoleon invaded Russia with his Grande Armee. France and Russia had similar sized populations during this era. Both sides had roughly up to 600,000 men in the field. As for quality, the Russian infantry at this time was known as being mediocre in the attack, but excellent and dogged in defense. There are theories on why this was the case, but the consensus seems to be that on average the Russian infantryman was less educated and therefore less capable of more complex attacking formations, and the Russian NCO corps less developed and able to coordinate on the attack, than the best armies in Europe. That being said, the Russians generally accounted themselves well fighting the French, and I would argue performed qualitatively better than the Prussians, Spanish, and Austrians against Napoleon. They weren't qualitatively better than the French, but then again no other country was, particularly when Napoleon was the commander. There's an argument for the British, who were excellent, but outside of Waterloo the British were fighting smaller battles and ones where Napoleon usually was not present.

The next big war for Russia was WW I. Here once again Russia's enemies feared her vast population and potential for putting large armies in the field. Russia also clearly was not up to the quality of German soldiers, usually losing when they fought the Germans, and often suffering disastrous defeats such as Masurian Lakes and Tannenberg. But like the French during Napoleon, it's important to recognize that the Germans were the cream of the crop in terms of European armies in WW I. The Russians also fought against the Ottomans and Austrians in WW I, and usually proved themselves qualitatively superior to these armies, frequently routing them.

My conclusion at least is that it's not accurate to say that the infantry formations of the Russian Empire were usually weaker. They were often qualitatively superior to their opponents, or even when not were not bad per se, just not as good as the cream of the crop. Other than these major battles I would add that the Russian Empire fairly consistently beat the Ottomans in their frequent wars from Catherine the Great on right up through WW I. I'm not all that knowledgeable on the Russo/Japanese War, maybe someone can fill in that blank.

Sources: Peter the Great, His Life & World, by Massie. The Campaigns of Napoleon, by Chandler. Prit Buttar's, War on the Eastern Front is a 4 book series on the Eastern Front in WW I and is the best English language military history of the war in the East in WW I that I have found.