Why did Justin Martyr speak so harshly about Christians who ate meat sacrificed to idols? In his Dialogue with Trypho, Chapter XXXV, Justin replies to Trypho's charge that Christians eat meat sacrificed to idols by saying that such people serve to show more distinctly who are the true followers of Jesus and exhort them to faithfulness, and that such people are wolves in sheep's clothing, causing schisms and heresies.

However, my reading of the New Testament creates the impression that abstinence from food sacrificed the idols was prescribed in the Jerusalem Council (Acts 15) on the basis of the preservation of unity, and Paul in 1 Corinthians 8 clarifies that food does not commend us to God, the idols have no real existence in themselves, but that we should use our freedom to not cause the "weaker brother" to stumble (evidently in this case, the one who through prior associations finds a problem with eating the meat). Paul seems to think that it is more of a question of the company one is keeping that might make the action sinful, as opposed to the action itself.

Trypho, as a Jew would have been such a person that the Christians should have at a minimum not publicly ate the meat around, and so they would be guilty of sin. But heresy? Wolves in sheep's clothing? Why does he not argue instead that these Christians are simply guilty of sin?
Justin Martyr (100–165), unfortunately, doesn't provide much additional insight into his position here or in his other writings.  However, his view was a common one in the 2nd and 3rd centuries, so we can better understand it by examining the writings of his contemporaries and immediately subsequent generations of church fathers.  Those holding this view include:

Irenaeus (?–202)
Tertullian (155–240)
Origen (184–254)

Irenaeus's treatment of this subject is similarly brief, but serves to demonstrate that Justin Martyr was not the only 2nd-century father who felt that eating meat sacrificed to idols was evidence of leaving the faith.  He writes:

Others [...] have introduced promiscuous intercourse and a plurality of wives, and are indifferent about eating meats sacrificed to idols, maintaining that God does not greatly regard such matters. But why continue? For it is an impracticable attempt to mention all those who, in one way or another, have fallen away from the truth.1

For the reasoning behind this view, we must turn to Tertullian and Origen.  The key passage they reference is 1 Corinthians 10; verses 19–21 being particularly relevant:

19 What do I imply then? That food offered to idols is anything, or that an idol is anything? 20 No, I imply that what pagans sacrifice they offer to demons and not to God. I do not want you to be participants with demons. 21 You cannot drink the cup of the Lord and the cup of demons. You cannot partake of the table of the Lord and the table of demons. [ESV]

Citing this passage, Tertullian argues that idolatry is demon worship and that therefore eating sacrificed meat is an example of eating from the table of demons:

the homage [idolators] render is to demons, who are the real occupants of these consecrated images, whether of dead men or (as they think) of gods. [...] We do not offer sacrifices to the gods, and we make no funeral oblations to the departed; nay, we do not partake of what is offered either in the one case or the other, for we cannot partake of God's feast and the feast of devils.2

Tertullian accepts 1 Corinthians 8:4, &quot;not that an idol is anything,&quot; but understands the verse to refer only to the image itself, for &quot;demons have abode in the images.&quot;2
Origen also uses the language of 1 Corinthians 10 to explain the apostolic prohibition on eating meat sacrificed to idols in Acts 15:28–29:

For that which is offered to idols is sacrificed to demons, and a man of God must not join the table of demons.3

Summary
Justin Martyr was not alone in strenuously objecting to the eating of meat sacrificed to idols.  The early fathers took the teaching of Acts 15 and 1 Corinthians 10 very seriously, and saw a close association between idols and demons.  As a result, they strongly opposed anyone who practiced or taught that eating meat sacrificed to idols was acceptable.

References:

Against Heresies, I.28.2
De Spectaculis, 12–13
Contra Celsus, VIII.30